Finite Group Databasebeta

← C2×#13119143 #16031970

Subgroups — C2×#13119143 #16031970

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88140C211yesmaximal, characteristic
2C22×#88183C211yesmaximal, characteristic
3C22×#88135C211yesmaximal, characteristic
4C23×#6101C211yesmaximal, characteristic, complemented
5#13119143C2116yesmaximal, direct product factor
6C2×#11718318C212yesmaximal, complemented
7C2×#11718336C212yesmaximal, complemented
8C2×#11718308C212yesmaximal, complemented
9C2×#11718604C211yesmaximal, characteristic, complemented
10C2×#11718328C212yesmaximal, complemented
11C2×#11718603C211yesmaximal, characteristic, complemented
12C2×C13×#381C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C24×Dic13C2211yescharacteristic
16C24×Dic13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C2×#88183—28no—
22C2×#88183C2218yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2212yes—
27C22×#6101—28no—
28C22×#6101C2212yes—
29C22×#6101C2212yes—
30C22×#6101C2212yes—
31C22×#6101C2211yescharacteristic
32C22×#6101C2212yes—
33C22×#6101C2218yescomplemented
34C22×C4×Dic13C2211yescharacteristic
35C2×#88140—28no—
36C2×#88140C2218yes—
37C2×#88135—28no—
38C2×#88135C2218yes—
39C13×#381C2218yescomplemented
40C2×C13×#95C2212yes—
41C2×C13×#95C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45#11718604C2218yescomplemented
46#11718603C2218yescomplemented
47#11718336C22116yescomplemented
48#11718328C22116yescomplemented
49#11718318C22116yescomplemented
50#11718308C22116yescomplemented
51C25×C13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C23×C4×C13—24no—
54C23×C4×C13—24no—
55C23×C4×C13—24no—
56C23×C4×C13C2314yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—24no—
62C22×C22⋊D13—24no—
63C22×C22⋊D13D418yes—
64C22×C22⋊D13C2314yes—
65C23×Dic13—28no—
66C23×Dic13—24no—
67C23×Dic13—24no—
68C23×Dic13—24no—
69C23×Dic13D418yes—
70C23×Dic13C2314yes—
71C23×Dic13C2312yes—
72C23×Dic13C2312yes—
73C23×Dic13C2314yes—
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C22×C4×D13—24no—
78C22×C4×D13—28no—
79C22×C4×D13C2314yes—
80C2×C13×C22⋊C4—24no—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4C2314yes—
83C2×C13×C22⋊C4C2314yes—
84C2×C22⋊Dic13—24no—
85C2×C22⋊Dic13C2314yes—
86#88183—232no—
87C2×#6103—28no—
88C2×#6103—28no—
89C2×#6103—24no—
90C2×#6103C2314yes—
91C2×#6103C2318yes—
92C2×#6103C2318yes—
93C2×C4⋊Dic13—28no—
94C2×C4⋊Dic13C2318yes—
95C2×#6101—24no—
96C2×#6101—28no—
97C2×#6101—28no—
98C2×#6101—232no—
99C2×#6101—28no—
100C2×#6101—28no—
101C2×#6101C2314yes—
102C2×#6101C2318yes—
103C2×#6101C2318yes—
104C2×#6101C2318yes—
105C2×#6101C2318yes—
106C2×C4×Dic13—24no—
107C2×C4×Dic13C2314yes—
108#88140—232no—
109#88135—232no—
110C13×#95C2318yes—
111C13×#95C2318yes—
112#88071C2318yes—
113#88071C2318yes—
114#88071C2318yes—
115C2×#2486—131nomaximal, Sylow
116C24×C13—24no—
117C24×C13—24no—
118C24×C13C2×D414yes—
119C24×C13C2×D414yes—
120C24×C13#4114yes—
121C24×C13C2412yes—
122C24×C13C2411yescharacteristic
123C23×D13—22no—
124C23×D13—24no—
125C23×D13—22no—
126C23×D13—24no—
127C23×D13C2×D414yes—
128C23×D13C2412yes—
129C22×C4×C13—22no—
130C22×C4×C13—28no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—28no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—28no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—24no—
142C22×C4×C13—416no—
143C22×C4×C13C2412yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2414yes—
147C2×C22⋊D13—232no—
148C2×C22⋊D13—28no—
149C2×C22⋊D13—28no—
150C2×C22⋊D13C2×D4116yes—
151C22×Dic13—22no—
152C22×Dic13—24no—
153C22×Dic13—22no—
154C22×Dic13—232no—
155C22×Dic13—216no—
156C22×Dic13—28no—
157C22×Dic13—28no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—28no—
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13—416no—
166C22×Dic13C2×D4116yes—
167C22×Dic13C2×D414yes—
168C22×Dic13C2×D414yes—
169C22×Dic13C2×D414yes—
170C22×Dic13#4118yes—
171C22×Dic13C2414yes—
172C22×Dic13C2414yes—
173C22×Dic13C2412yes—
174C22×Dic13C2412yes—
175C22×Dic13C2412yes—
176C2×C4×D13—28no—
177C2×C4×D13—216no—
178C2×C4×D13—416no—
179C13×C22⋊C4—28no—
180C13×C22⋊C4—28no—
181C22⋊Dic13—28no—
182#6103—216no—
183#6103—216no—
184#6103—28no—
185C4⋊Dic13—216no—
186#6101—28no—
187#6101—216no—
188#6101—216no—
189#6101—216no—
190#6101—216no—
191C4×Dic13—28no—
192C22×#123—131no—
193C22×#123—131no—
194C22×C4×D4—131no—
195C23×C4⋊C4—131no—
196#2486—1316no—
197C2×#398—132no—
198C2×#397—132no—
199C2×#389—132no—
200C2×#381—131no—
201C2×#381D1311yescharacteristic, complemented
202C2×#380—132no—
203C2×#380—131no—
204C23×C13—28no—
205C23×C13—28no—
206C23×C13—216no—
207C23×C13—216no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13#121116yes—
211C23×C13C22×D414yes—
212C23×C13C22×D414yes—
213C23×C13C22×D412yes—
214C23×C13C22×D412yes—
215C23×C13C2×#4114yes—
216C23×C13C2×#4112yes—
217C23×C13C2×#4114yes—
218C23×C132−1+414yes—
219C23×C13C2511yescharacteristic
220C22×D13—28no—
221C22×D13—216no—
222C22×D13—22no—
223C22×D13—24no—
224C22×D13—22no—
225C22×D13—24no—
226C22×D13—44no—
227C22×D13—44no—
228C22×D13—48no—
229C22×D13C22×D414yes—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—416no—
241C2×C4×C13—48no—
242C2×C4×C13—44no—
243C2×C4×C13—44no—
244C2×C4×C13—48no—
245C22⋊D13—232no—
246C2×Dic13—28no—
247C2×Dic13—28no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—22no—
251C2×Dic13—232no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—416no—
259C2×Dic13—48no—
260C2×Dic13—48no—
261C2×Dic13#123116yescomplemented
262C2×Dic13C22×D414yes—
263C2×Dic13C22×D414yes—
264C2×Dic13C22×D414yes—
265C2×Dic13C2×#4118yes—
266C4×D13—416no—
267C23×D4—131no—
268C24×C4—131no—
269C24×C4—131no—
270C24×C4—131no—
271C24×C4C2×D1311yescharacteristic
272C2×#123—138no—
273C2×#123—138no—
274C2×#123—268no—
275C2×#123—268no—
276C2×C4×D4—138no—
277C2×C4×D4—268no—
278C22×C4⋊C4—132no—
279C22×C4⋊C4—131no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—138no—
284C22×C4⋊C4—132no—
285C22×C4⋊C4—268no—
286C22×C22⋊C4—131no—
287C22×C22⋊C4—131no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4C2×D1311yescharacteristic
291C22×C22⋊C4C2×D1311yescharacteristic
292C22×C42—131no—
293#398—1316no—
294#397—1316no—
295#389—1316no—
296#381—138no—
297#381C2×D1318yescomplemented
298#380—138no—
299#380—1316no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95C2×D1312yes—
304C2×#95C2×D1312yes—
305C22×C13—24no—
306C22×C13—24no—
307C22×C13—28no—
308C22×C13—28no—
309C22×C13—232no—
310C22×C13C2×#12118yes—
311C22×C13C2×#12114yes—
312C22×C13C2×#12314yes—
313C22×C13#53614yes—
314C22×C13#54718yes—
315C22×C13#55218yes—
316C22×C13C23×D411yescharacteristic
317C22×C13C23×D411yescharacteristic
318C22×C13C22×#4111yescharacteristic
319C22×C13C22×#4112yes—
320C22×C13C2×2−1+412yes—
321C2×D13—24no—
322C2×D13—28no—
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—44no—
326C2×D13—416no—
327C4×C13—44no—
328C4×C13—42no—
329C4×C13—42no—
330C4×C13—44no—
331Dic13—24no—
332Dic13—24no—
333Dic13—44no—
334Dic13—44no—
335Dic13C2×#12318yescomplemented
336C25—131no—
337C25C22×D1311yescharacteristic
338C22×D4—138no—
339C22×D4—134no—
340C22×D4—264no—
341C22×D4—264no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—24no—
345C23×C4—131no—
346C23×C4—138no—
347C23×C4—134no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—134no—
351C23×C4—132no—
352C23×C4—132no—
353C23×C4—134no—
354C23×C4—264no—
355C23×C4—268no—
356C23×C4—268no—
357C23×C4—264no—
358C23×C4—264no—
359C23×C4—264no—
360C23×C4C22×D1314yes—
361C23×C4C22×D1312yes—
362C23×C4C22×D1311yescharacteristic
363C23×C4C22×D1312yes—
364C23×C4C22×D1311yescharacteristic
365#123—2632no—
366#123—2632no—
367C4×D4—2632no—
368C2×C4⋊C4—138no—
369C2×C4⋊C4—138no—
370C2×C4⋊C4—134no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—138no—
374C2×C4⋊C4—268no—
375C2×C4⋊C4—268no—
376C2×C4⋊C4—2632no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—268no—
380C2×C4⋊C4—268no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—134no—
384C2×C22⋊C4—134no—
385C2×C22⋊C4—138no—
386C2×C22⋊C4—138no—
387C2×C22⋊C4—264no—
388C2×C22⋊C4—268no—
389C2×C22⋊C4—268no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4C22×D1314yes—
392C2×C22⋊C4C22×D1314yes—
393C2×C42—134no—
394C2×C42—264no—
395#95—138no—
396#95—138no—
397#95—138no—
398#95C22×D1318yes—
399#95C22×D1318yes—
400C2×C13—28no—
401C2×C13#248618yescomplemented
402C2×C13C22×#12111yescharacteristic
403C2×C13C22×#12311yescharacteristic
404C2×C13C2×#53611yescharacteristic
405C2×C13C2×#54712yes—
406C2×C13C2×#55212yes—
407D13—44no—
408C24—24no—
409C24—24no—
410C24—134no—
411C24—132no—
412C24—262no—
413C24—262no—
414C24—264no—
415C24—264no—
416C24#612714yes—
417C24D4×D1314yes—
418C24D4×D1314yes—
419C24C23×D1312yes—
420C24C23×D1311yescharacteristic
421C2×D4—1316no—
422C2×D4—2632no—
423C2×D4—268no—
424C2×D4—268no—
425C22×C4—28no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—28no—
432C22×C4—24no—
433C22×C4—28no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—416no—
439C22×C4—134no—
440C22×C4—138no—
441C22×C4—132no—
442C22×C4—134no—
443C22×C4—134no—
444C22×C4—1316no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—134no—
448C22×C4—134no—
449C22×C4—268no—
450C22×C4—2616no—
451C22×C4—2632no—
452C22×C4—2616no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—264no—
456C22×C4—268no—
457C22×C4—264no—
458C22×C4—264no—
459C22×C4—264no—
460C22×C4—268no—
461C22×C4—264no—
462C22×C4—268no—
463C22×C4—264no—
464C22×C4—264no—
465C22×C4—5216no—
466C22×C4—5216no—
467C22×C4C23×D1312yes—
468C22×C4C23×D1312yes—
469C22×C4C23×D1314yes—
470C22×C4C23×D1314yes—
471C4⋊C4—2616no—
472C4⋊C4—2616no—
473C4⋊C4—268no—
474C4⋊C4—2616no—
475C4⋊C4—2616no—
476C4⋊C4—2616no—
477C22⋊C4—28no—
478C22⋊C4—28no—
479C22⋊C4—268no—
480C22⋊C4—2616no—
481C22⋊C4—2616no—
482C22⋊C4—268no—
483C42—268no—
484C13C2×#248611yescharacteristic, complemented, Sylow
485C23—216no—
486C23—28no—
487C23—28no—
488C23—216no—
489C23—24no—
490C23—24no—
491C23—134no—
492C23—268no—
493C23—2616no—
494C23—262no—
495C23—262no—
496C23—264no—
497C23—264no—
498C23—528no—
499C23—524no—
500C23—524no—
501C23#88138116yes—
502C23C2×#612714yes—
503C23C2×#612712yes—
504C23C2×D4×D1314yes—
505C23C2×D4×D1314yes—
506C23C2×D4×D1312yes—
507C23C2×D4×D1312yes—
508C23#41×D1314yes—
509C23#8825714yes—
510C23C24×D1311yescharacteristic
511D4—2632no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—416no—
523C2×C4—48no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—48no—
527C2×C4—1316no—
528C2×C4—134no—
529C2×C4—138no—
530C2×C4—134no—
531C2×C4—134no—
532C2×C4—2632no—
533C2×C4—268no—
534C2×C4—268no—
535C2×C4—262no—
536C2×C4—262no—
537C2×C4—264no—
538C2×C4—264no—
539C2×C4—264no—
540C2×C4—264no—
541C2×C4—264no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—5216no—
545C2×C4—5216no—
546C2×C4—528no—
547C2×C4—528no—
548C22—28no—
549C22—24no—
550C22—28no—
551C22—232no—
552C22—24no—
553C22—268no—
554C22—264no—
555C22—522no—
556C22—524no—
557C22—5216no—
558C22—522no—
559C22C2×#8813818yes—
560C22C2×#8813814yes—
561C22#1171923618yes—
562C22#1171935314yes—
563C22D13×#12314yes—
564C22#1171936018yes—
565C22C22×#612711yescharacteristic
566C22C22×D4×D1311yescharacteristic
567C22C22×D4×D1311yescharacteristic
568C22C2×#41×D1312yes—
569C22C2×#8825712yes—
570C4—44no—
571C4—44no—
572C4—42no—
573C4—42no—
574C4—138no—
575C4—264no—
576C4—264no—
577C4—524no—
578C4—524no—
579C2—28no—
580C2—524no—
581C2#1311914318yesdirect product factor
582C2C22×#8813811yescharacteristic
583C2C2×D13×#12311yescharacteristic
584C2C2×#1171935311yescharacteristic
585C2C2×#1171936012yes—
586C2C2×#1171923612yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#381C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#381D13
hypocenterC13C2×#2486
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. C23×#6101C2semidirect
5. #13119143C2direct (N × H)
6. C2×#11718318C2semidirect
7. C2×#11718336C2semidirect
8. C2×#11718308C2semidirect
9. C2×#11718604C2semidirect
10. C2×#11718328C2semidirect
11. C2×#11718603C2semidirect
12. C2×C13×#381C2semidirect
33. C22×#6101C22semidirect
39. C13×#381C22semidirect
45. #11718604C22semidirect
46. #11718603C22semidirect
47. #11718336C22semidirect
48. #11718328C22semidirect
49. #11718318C22semidirect
50. #11718308C22semidirect
201. C2×#381D13semidirect
261. C2×Dic13#123semidirect
297. #381C2×D13semidirect
335. Dic13C2×#123semidirect
401. C2×C13#2486semidirect
484. C13C2×#2486semidirect
581. C2#13119143direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881402
C22×#881832
C22×#881352
C23×#61012
#131191432
C2×#117183182
C2×#117183362
C2×#117183082
C2×#117186042
C2×#117183282
C2×#117186032
C2×C13×#3812
C2×#248613