Finite Group Databasebeta

← C2×#13119988 #16033290

Subgroups — C2×#13119988 #16033290

Order 3328.

4166 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13119988C2116yesmaximal, direct product factor
4C2×#11718654C211yesmaximal, characteristic, complemented
5C2×#11718334C211yesmaximal, characteristic, complemented
6C2×#11718608C211yesmaximal, characteristic, complemented
7C2×#11718612C212yesmaximal, complemented
8C2×#11718331C212yesmaximal, complemented
9C2×#11718325C212yesmaximal, complemented
10C2×#11718616C212yesmaximal
11C2×#11718327C211yesmaximal, characteristic, complemented
12C2×C13×#397C211yesmaximal, characteristic, complemented
13C25×D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×Dic26C2211yescharacteristic, complemented
17C22×C13×C4⋊C4C2211yescharacteristic, complemented
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2212yes—
22C22×#6103C2212yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2212yes—
28C22×C4⋊Dic13C2212yescomplemented
29C22×C4×Dic13C2212yescomplemented
30C2×#88151—28no—
31C2×#88151C2218yescomplemented
32C2×C22⋊C4×D13—28no—
33C2×C22⋊C4×D13C2218yes—
34C13×#397C2218yescomplemented
35C2×C13×#95C2212yescomplemented
36C2×C13×#95C2211yescharacteristic, complemented
37C2×#88071C2212yescomplemented
38C2×#88071C2212yescomplemented
39C2×#88071C2212yescomplemented
40C2×#88071C2211yescharacteristic, complemented
41#11718654C2218yescomplemented
42#11718616C22116yes—
43#11718612C22116yescomplemented
44#11718608C2218yescomplemented
45#11718334C2218yescomplemented
46#11718331C22116yescomplemented
47#11718327C2218yescomplemented
48#11718325C22116yescomplemented
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×Dic13C2312yes—
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C22×C4×D13—24no—
67C22×C4×D13—28no—
68C22×C4×D13—44no—
69C22×C4×D13D418yes—
70C22×C4×D13C2314yes—
71C22×C4×D13C2314yes—
72C22×Dic26—24no—
73C22×Dic26—44no—
74C22×Dic26C2314yescomplemented
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4C2314yescomplemented
77C2×C13×C22⋊C4—28no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4C2314yes—
80C2×C13×C22⋊C4C2318yes—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—44no—
83C2×C22⋊Dic13C2314yes—
84C2×C22⋊Dic13C2318yes—
85C2×#6103—28no—
86C2×#6103—28no—
87C2×#6103—28no—
88C2×#6103—24no—
89C2×#6103—24no—
90C2×#6103—44no—
91C2×#6103C2314yes—
92C2×#6103C2314yes—
93C2×#6103C2318yes—
94C2×#6103C2318yes—
95C2×#6103C2318yes—
96C2×#6103C2318yes—
97C2×C4⋊Dic13—28no—
98C2×C4⋊Dic13C2318yescomplemented
99C2×C4×Dic13—44no—
100C2×C4×Dic13C2318yescomplemented
101#88151—232no—
102C22⋊C4×D13—232no—
103C13×#95C2318yescomplemented
104C13×#95C2314yescomplemented
105#88071C2318yescomplemented
106#88071C2318yescomplemented
107#88071C2318yescomplemented
108#88071C2314yescomplemented
109C2×#2561—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×C13C2412yes—
150C22×C4×C13C2414yes—
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×Dic13C2412yes—
164C22×Dic13C2414yes—
165C22×Dic13C2414yes—
166C22×Dic13C2412yes—
167C2×C4×D13—28no—
168C2×C4×D13—216no—
169C2×C4×D13—416no—
170C2×C4×D13—48no—
171C2×C4×D13—416no—
172C2×C4×D13C2×D4116yes—
173C2×Dic26—28no—
174C2×Dic26—48no—
175C2×Dic26—416no—
176C13×C4⋊C4—28no—
177C13×C22⋊C4—216no—
178C13×C22⋊C4—28no—
179C22⋊Dic13—28no—
180C22⋊Dic13—48no—
181#6103—216no—
182#6103—216no—
183#6103—216no—
184#6103—28no—
185#6103—28no—
186#6103—48no—
187C4⋊Dic13—216no—
188C4×Dic13—48no—
189C22×C22⋊Q8—131no—
190C23×C22⋊C4—131no—
191#2561—1316no—
192C2×#397—131no—
193C2×#397D1311yescharacteristic, complemented
194C2×#393—131no—
195C2×#393—131no—
196C2×#388—132no—
197C2×#388—132no—
198C2×#381—132no—
199C2×#379—132no—
200C2×C4×C22⋊C4—131no—
201C23×C13—28no—
202C23×C13—216no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—24no—
206C23×C13—24no—
207C23×C13—44no—
208C23×C13—44no—
209C23×C13—48no—
210C23×C13C22×D412yes—
211C23×C13C2×#4114yes—
212C23×C13C2×#4112yes—
213C23×C13C2×#4112yes—
214C23×C13C2×#4114yes—
215C23×C13H(5,𝔽2)14yes—
216C23×C13C2511yescharacteristic
217C22×D13—28no—
218C22×D13—28no—
219C22×D13—216no—
220C22×D13—216no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—24no—
224C22×D13—232no—
225C22×D13—28no—
226C22×D13—216no—
227C22×D13—22no—
228C22×D13—22no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—432no—
232C22×D13—432no—
233C22×D13—4128no—
234C22×D13—416no—
235C22×D13—44no—
236C22×D13—44no—
237C22×D13—48no—
238C22×D13—416no—
239C22×D13#124116yes—
240C22×D13C22×D414yes—
241C22×D13C2×#4114yes—
242C22×D13C2×#4118yes—
243C2×C4×C13—28no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—48no—
254C2×C4×C13—44no—
255C2×C4×C13—48no—
256C2×C4×C13C22×D414yes—
257C2×Dic13—28no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—22no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—44no—
268C2×Dic13—48no—
269C2×Dic13—48no—
270C2×Dic13C22×D414yes—
271C4×D13—416no—
272C4×D13—416no—
273Dic26—416no—
274C26—131no—
275C23×Q8—131no—
276C24×C4—131no—
277C24×C4—131no—
278C2×C22⋊Q8—138no—
279C2×C22⋊Q8—268no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4C2×D1311yescharacteristic, complemented
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—132no—
290C22×C22⋊C4—138no—
291C22×C22⋊C4—268no—
292C22×C22⋊C4C2×D1311yescharacteristic
293C22×C22⋊C4C2×D1312yes—
294C22×C42—132no—
295#397—138no—
296#397C2×D1318yescomplemented
297#393—138no—
298#393—138no—
299#388—1316no—
300#388—1316no—
301#381—1316no—
302#379—1316no—
303C4×C22⋊C4—138no—
304C2×#95—131no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95C2×D1311yescharacteristic, complemented
309C2×#95C2×D1312yescomplemented
310C22×C13—24no—
311C22×C13—28no—
312C22×C13—416no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—44no—
316C22×C13#52514yes—
317C22×C13C2×#12414yes—
318C22×C13#53414yes—
319C22×C13#55118yes—
320C22×C13#55118yes—
321C22×C13C23×D411yescharacteristic
322C22×C13C22×#4111yescharacteristic
323C22×C13C22×#4111yescharacteristic
324C22×C13C22×#4112yes—
325C22×C13C2×H(5,𝔽2)12yes—
326C2×D13—232no—
327C2×D13—24no—
328C2×D13—24no—
329C2×D13—28no—
330C2×D13—28no—
331C2×D13—24no—
332C2×D13—28no—
333C2×D13—464no—
334C2×D13—416no—
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—44no—
338C2×D13C2×#12418yes—
339C4×C13—24no—
340C4×C13—44no—
341C4×C13—42no—
342C4×C13—44no—
343Dic13—24no—
344Dic13—42no—
345Dic13—44no—
346Dic13—44no—
347C25—131no—
348C25—131no—
349C25—134no—
350C25—264no—
351C25—264no—
352C25—268no—
353C25—264no—
354C25—524no—
355C25C22×D1311yescharacteristic
356C22×Q8—134no—
357C22×Q8—264no—
358C22×Q8—524no—
359C23×C4—131no—
360C23×C4—138no—
361C23×C4—134no—
362C23×C4—132no—
363C23×C4—132no—
364C23×C4—131no—
365C23×C4—134no—
366C23×C4—264no—
367C23×C4—268no—
368C23×C4—524no—
369C23×C4C22×D1312yes—
370C23×C4C22×D1312yes—
371C23×C4C22×D1311yescharacteristic
372C23×C4C22×D1311yescharacteristic
373C22⋊Q8—2632no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—138no—
376C2×C4⋊C4—268no—
377C2×C4⋊C4C22×D1314yescomplemented
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—134no—
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—138no—
388C2×C22⋊C4—2632no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—268no—
391C2×C22⋊C4—268no—
392C2×C22⋊C4—268no—
393C2×C22⋊C4—264no—
394C2×C22⋊C4—264no—
395C2×C22⋊C4—524no—
396C2×C22⋊C4—524no—
397C2×C22⋊C4C22×D1314yes—
398C2×C22⋊C4C22×D1318yes—
399C2×C42—138no—
400C2×C42—524no—
401#95—134no—
402#95—138no—
403#95—138no—
404#95—138no—
405#95C22×D1314yescomplemented
406#95C22×D1318yescomplemented
407C2×C13—44no—
408C2×C13#256118yescomplemented
409C2×C13C2×#52511yescharacteristic
410C2×C13C22×#12411yescharacteristic
411C2×C13C2×#53411yescharacteristic
412C2×C13C2×#55112yes—
413C2×C13C2×#55112yes—
414D13—28no—
415D13—44no—
416C24—22no—
417C24—22no—
418C24—24no—
419C24—24no—
420C24—134no—
421C24—138no—
422C24—132no—
423C24—134no—
424C24—132no—
425C24—268no—
426C24—268no—
427C24—2616no—
428C24—2632no—
429C24—262no—
430C24—262no—
431C24—264no—
432C24—262no—
433C24—268no—
434C24—262no—
435C24—264no—
436C24—264no—
437C24—528no—
438C24—5232no—
439C24—5216no—
440C24—5232no—
441C24—5216no—
442C24#612914yes—
443C24C23×D1312yes—
444C24C23×D1311yescharacteristic
445C2×Q8—268no—
446C2×Q8—528no—
447C2×Q8—5216no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—134no—
458C22×C4—132no—
459C22×C4—1316no—
460C22×C4—132no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—268no—
464C22×C4—2616no—
465C22×C4—264no—
466C22×C4—262no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—264no—
471C22×C4—264no—
472C22×C4—264no—
473C22×C4—264no—
474C22×C4—5216no—
475C22×C4—528no—
476C22×C4—5216no—
477C22×C4D4×D1314yes—
478C22×C4C23×D1312yes—
479C22×C4C23×D1314yes—
480C22×C4C23×D1314yes—
481C22×C4C23×D1312yes—
482C4⋊C4—28no—
483C4⋊C4—2616no—
484C22⋊C4—216no—
485C22⋊C4—28no—
486C22⋊C4—268no—
487C22⋊C4—2616no—
488C22⋊C4—2616no—
489C22⋊C4—2616no—
490C22⋊C4—268no—
491C22⋊C4—268no—
492C22⋊C4—528no—
493C22⋊C4—528no—
494C42—528no—
495C13C2×#256111yescharacteristic, complemented, Sylow
496C23—28no—
497C23—216no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—24no—
502C23—44no—
503C23—44no—
504C23—48no—
505C23—1316no—
506C23—134no—
507C23—138no—
508C23—134no—
509C23—2632no—
510C23—268no—
511C23—268no—
512C23—2616no—
513C23—262no—
514C23—262no—
515C23—264no—
516C23—2616no—
517C23—268no—
518C23—262no—
519C23—262no—
520C23—264no—
521C23—264no—
522C23—2616no—
523C23—5232no—
524C23—5216no—
525C23—5232no—
526C23—5216no—
527C23—52128no—
528C23—524no—
529C23—528no—
530C23—524no—
531C23C2×D4×D1312yes—
532C23C2×#612914yes—
533C23C2×#612912yes—
534C23#41×D1312yes—
535C23#41×D1314yes—
536C23#8825614yes—
537C23C24×D1311yescharacteristic
538Q8—5216no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—48no—
550C2×C4—48no—
551C2×C4—44no—
552C2×C4—134no—
553C2×C4—268no—
554C2×C4—264no—
555C2×C4—262no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—5216no—
564C2×C4—5216no—
565C2×C4—528no—
566C2×C4—524no—
567C2×C4—528no—
568C2×C4C2×D4×D1314yes—
569C22—28no—
570C22—24no—
571C22—44no—
572C22—42no—
573C22—42no—
574C22—416no—
575C22—138no—
576C22—268no—
577C22—268no—
578C22—264no—
579C22—264no—
580C22—2632no—
581C22—268no—
582C22—264no—
583C22—5264no—
584C22—524no—
585C22—522no—
586C22—522no—
587C22—5216no—
588C22#1171931114yes—
589C22#1171935814yes—
590C22#1171936318yes—
591C22D13×#12414yes—
592C22#1171941018yes—
593C22C22×D4×D1311yescharacteristic
594C22C22×#612911yescharacteristic
595C22C2×#41×D1312yes—
596C22C2×#41×D1311yescharacteristic
597C22C2×#8825612yes—
598C4—24no—
599C4—44no—
600C4—44no—
601C4—42no—
602C4—264no—
603C4—524no—
604C4—522no—
605C4—524no—
606C2—44no—
607C2—268no—
608C2—524no—
609C2#1311998818yesdirect product factor
610C2C2×#1171931111yescharacteristic
611C2C2×D13×#12411yescharacteristic
612C2C2×#1171935811yescharacteristic
613C2C2×#1171936312yes—
614C2C2×#1171941012yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#397C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#397D13
hypocenterC13C2×#2561
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
3. #13119988C2direct (N × H)
4. C2×#11718654C2semidirect
5. C2×#11718334C2semidirect
6. C2×#11718608C2semidirect
7. C2×#11718612C2semidirect
8. C2×#11718331C2semidirect
9. C2×#11718325C2semidirect
11. C2×#11718327C2semidirect
12. C2×C13×#397C2semidirect
16. C23×Dic26C22semidirect
17. C22×C13×C4⋊C4C22semidirect
28. C22×C4⋊Dic13C22semidirect
29. C22×C4×Dic13C22semidirect
31. C2×#88151C22semidirect
34. C13×#397C22semidirect
35. C2×C13×#95C22semidirect
36. C2×C13×#95C22semidirect
37. C2×#88071C22semidirect
38. C2×#88071C22semidirect
39. C2×#88071C22semidirect
40. C2×#88071C22semidirect
41. #11718654C22semidirect
43. #11718612C22semidirect
44. #11718608C22semidirect
45. #11718334C22semidirect
46. #11718331C22semidirect
47. #11718327C22semidirect
48. #11718325C22semidirect
74. C22×Dic26C23semidirect
76. C2×C13×C4⋊C4C23semidirect
98. C2×C4⋊Dic13C23semidirect
100. C2×C4×Dic13C23semidirect
103. C13×#95C23semidirect
104. C13×#95C23semidirect
105. #88071C23semidirect
106. #88071C23semidirect
107. #88071C23semidirect
108. #88071C23semidirect
193. C2×#397D13semidirect
281. C22×C4⋊C4C2×D13semidirect
296. #397C2×D13semidirect
308. C2×#95C2×D13semidirect
309. C2×#95C2×D13semidirect
377. C2×C4⋊C4C22×D13semidirect
405. #95C22×D13semidirect
406. #95C22×D13semidirect
408. C2×C13#2561semidirect
495. C13C2×#2561semidirect
609. C2#13119988direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×C22⋊C4×D132
#131199882
C2×#117186542
C2×#117183342
C2×#117186082
C2×#117186122
C2×#117183312
C2×#117183252
C2×#117186162
C2×#117183272
C2×C13×#3972
C2×#256113