Finite Group Databasebeta

← C2×#13118245 #16031622

Subgroups — C2×#13118245 #16031622

Order 3328.

3570 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88140C211yesmaximal, characteristic
2C22×#88183C211yesmaximal, characteristic
3C22×#88131C211yesmaximal, characteristic, complemented
4C23×#6101C211yesmaximal, characteristic, complemented
5#13118245C2116yesmaximal, direct product factor
6C2×#11718318C212yesmaximal, complemented
7C2×#11718337C212yesmaximal, complemented
8C2×#11718308C212yesmaximal, complemented
9C2×#11718330C212yesmaximal, complemented
10C2×#11718619C211yesmaximal, characteristic
11C2×#11718607C211yesmaximal, characteristic, complemented
12C2×C13×#381C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C24×Dic13C2211yescharacteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C2×#88183—28no—
21C2×#88183C2218yes—
22C22×#6103C2212yes—
23C22×#6103C2211yescharacteristic
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101—28no—
29C22×#6101C2212yes—
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C22×#6101C2212yes—
33C22×#6101C2212yes—
34C22×#6101C2218yescomplemented
35C22×C4×Dic13C2212yes—
36C2×#88140—28no—
37C2×#88140C2218yes—
38C2×#88131—28no—
39C2×#88131C2218yescomplemented
40C13×#381C2218yescomplemented
41C2×C13×#95C2212yes—
42C2×C13×#95C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45#11718619C2218yes—
46#11718607C2218yescomplemented
47#11718337C22116yescomplemented
48#11718330C22116yescomplemented
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×C13C2312yes—
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—24no—
62C22×C22⋊D13—24no—
63C22×C22⋊D13—24no—
64C22×C22⋊D13C2314yes—
65C23×Dic13—24no—
66C23×Dic13—24no—
67C23×Dic13—24no—
68C23×Dic13—28no—
69C23×Dic13D418yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2314yes—
72C23×Dic13C2314yes—
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2312yes—
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2312yes—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4C2314yes—
80C2×C13×C22⋊C4C2314yes—
81C2×C22⋊Dic13D418yes—
82C2×C22⋊Dic13C2314yes—
83#88183—232no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—28no—
87C2×#6103—28no—
88C2×#6103C2314yes—
89C2×#6103C2314yes—
90C2×#6103C2318yes—
91C2×#6103C2318yes—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13C2314yes—
95C2×C4⋊Dic13C2314yes—
96C2×#6101—28no—
97C2×#6101—28no—
98C2×#6101—28no—
99C2×#6101—232no—
100C2×#6101—28no—
101C2×#6101—28no—
102C2×#6101C2318yes—
103C2×#6101C2318yes—
104C2×#6101C2318yes—
105C2×#6101C2318yes—
106C2×#6101C2318yes—
107C2×C4×Dic13—28no—
108C2×C4×Dic13C2318yes—
109#88140—232no—
110#88131—232no—
111C13×#95C2318yes—
112C13×#95C2318yes—
113#88071C2318yes—
114#88071C2318yes—
115C2×#2413—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—22no—
125C23×D13—24no—
126C23×D13—22no—
127C23×D13—24no—
128C23×D13C2412yes—
129C22×C4×C13—24no—
130C22×C4×C13—28no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
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×C13C2414yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2412yes—
147C2×C22⋊D13—28no—
148C2×C22⋊D13—28no—
149C2×C22⋊D13—28no—
150C2×C22⋊D13—416no—
151C22×Dic13—232no—
152C22×Dic13—232no—
153C22×Dic13—28no—
154C22×Dic13—22no—
155C22×Dic13—28no—
156C22×Dic13—22no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—28no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—216no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13C2×D4116yes—
169C22×Dic13C2×D418yes—
170C22×Dic13C2×D414yes—
171C22×Dic13C2×D414yes—
172C22×Dic13#4118yes—
173C22×Dic13C2412yes—
174C22×Dic13C2414yes—
175C22×Dic13C2412yes—
176C22×Dic13C2412yes—
177C22×Dic13C2414yes—
178C13×C22⋊C4—28no—
179C13×C22⋊C4—28no—
180C22⋊Dic13C2×D4116yes—
181#6103—28no—
182#6103—28no—
183#6103—216no—
184#6103—216no—
185C4⋊Dic13—28no—
186C4⋊Dic13—28no—
187#6101—216no—
188#6101—216no—
189#6101—216no—
190#6101—216no—
191#6101—216no—
192C4×Dic13—216no—
193C22×#123—131no—
194C22×#123—131no—
195C22×#117—131no—
196C23×C4⋊C4—131no—
197#2413—1316no—
198C2×#398—132no—
199C2×#396—132no—
200C2×#389—132no—
201C2×#388—132no—
202C2×#386—131no—
203C2×#385—131no—
204C2×#381D1311yescharacteristic, complemented
205C23×C13—28no—
206C23×C13—28no—
207C23×C13—216no—
208C23×C13—216no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13#121116yes—
212C23×C13C22×D414yes—
213C23×C13C22×D414yes—
214C23×C13C22×D412yes—
215C23×C13C22×D412yes—
216C23×C13C2×#4114yes—
217C23×C13C2×#4112yes—
218C23×C13C2×#4114yes—
219C23×C132−1+414yes—
220C23×C13C2511yescharacteristic
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—24no—
224C22×D13—22no—
225C22×D13—24no—
226C22×D13—44no—
227C22×D13—44no—
228C22×D13—44no—
229C22×D13—48no—
230C22×D13—48no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—416no—
242C2×C4×C13—48no—
243C2×C4×C13—44no—
244C2×C4×C13—44no—
245C2×C4×C13—48no—
246C22⋊D13—416no—
247C2×Dic13—232no—
248C2×Dic13—232no—
249C2×Dic13—28no—
250C2×Dic13—28no—
251C2×Dic13—216no—
252C2×Dic13—216no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—44no—
265C2×Dic13C22×D418yes—
266C2×Dic13C22×D414yes—
267C2×Dic13C22×D414yes—
268C2×Dic13C2×#4118yes—
269C23×D4—131no—
270C24×C4—131no—
271C24×C4—131no—
272C24×C4C2×D1311yescharacteristic
273C2×#123—138no—
274C2×#123—138no—
275C2×#123—268no—
276C2×#123—268no—
277C2×#117—138no—
278C2×#117—268no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4—138no—
285C22×C4⋊C4—131no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—268no—
288C22×C22⋊C4—131no—
289C22×C22⋊C4—131no—
290C22×C22⋊C4—132no—
291C22×C22⋊C4—132no—
292C22×C22⋊C4—131no—
293C22×C22⋊C4C2×D1311yescharacteristic
294C22×C22⋊C4C2×D1311yescharacteristic
295C22×C42—132no—
296#398—1316no—
297#396—1316no—
298#389—1316no—
299#388—1316no—
300#386—138no—
301#385—138no—
302#381C2×D1318yescomplemented
303C2×#95—132no—
304C2×#95—132no—
305C2×#95C2×D1312yes—
306C2×#95C2×D1312yes—
307C22×C13—24no—
308C22×C13—232no—
309C22×C13—24no—
310C22×C13—28no—
311C22×C13—28no—
312C22×C13C2×#12118yes—
313C22×C13C2×#12114yes—
314C22×C13#52514yes—
315C22×C13#53614yes—
316C22×C13#54718yes—
317C22×C13#55218yes—
318C22×C13C23×D411yescharacteristic
319C22×C13C23×D411yescharacteristic
320C22×C13C22×#4111yescharacteristic
321C22×C13C22×#4112yes—
322C22×C13C2×2−1+412yes—
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—44no—
327C2×D13—44no—
328C2×D13—88no—
329C4×C13—44no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—44no—
333Dic13—24no—
334Dic13—24no—
335Dic13—28no—
336Dic13—28no—
337Dic13—42no—
338C25—131no—
339C25C22×D1311yescharacteristic
340C22×D4—134no—
341C22×D4—264no—
342C22×D4—264no—
343C22×D4—264no—
344C23×C4—24no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—138no—
348C23×C4—134no—
349C23×C4—132no—
350C23×C4—131no—
351C23×C4—132no—
352C23×C4—131no—
353C23×C4—134no—
354C23×C4—131no—
355C23×C4—268no—
356C23×C4—264no—
357C23×C4—264no—
358C23×C4—264no—
359C23×C4C22×D1314yes—
360C23×C4C22×D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1312yes—
363C23×C4C22×D1312yes—
364#123—2632no—
365#123—2632no—
366#117—2632no—
367C2×C4⋊C4—138no—
368C2×C4⋊C4—138no—
369C2×C4⋊C4—138no—
370C2×C4⋊C4—138no—
371C2×C4⋊C4—134no—
372C2×C4⋊C4—134no—
373C2×C4⋊C4—138no—
374C2×C4⋊C4—268no—
375C2×C4⋊C4—268no—
376C2×C4⋊C4—2632no—
377C2×C4⋊C4—268no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—268no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—138no—
385C2×C22⋊C4—134no—
386C2×C22⋊C4—134no—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—134no—
389C2×C22⋊C4—138no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—264no—
392C2×C22⋊C4—268no—
393C2×C22⋊C4—268no—
394C2×C22⋊C4C22×D1314yes—
395C2×C22⋊C4C22×D1314yes—
396C2×C42—138no—
397C2×C42—268no—
398#95—138no—
399#95—138no—
400#95C22×D1318yes—
401#95C22×D1318yes—
402C2×C13—28no—
403C2×C13#241318yescomplemented
404C2×C13C22×#12111yescharacteristic
405C2×C13C2×#52511yescharacteristic
406C2×C13C2×#53611yescharacteristic
407C2×C13C2×#54712yes—
408C2×C13C2×#55212yes—
409D13—82no—
410C24—24no—
411C24—24no—
412C24—132no—
413C24—262no—
414C24—262no—
415C24—262no—
416C24—264no—
417C24—264no—
418C24#612714yes—
419C24D4×D1314yes—
420C24D4×D1314yes—
421C24C23×D1312yes—
422C24C23×D1311yescharacteristic
423C2×D4—268no—
424C2×D4—268no—
425C2×D4—268no—
426C2×D4—5216no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—28no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—416no—
441C22×C4—138no—
442C22×C4—134no—
443C22×C4—134no—
444C22×C4—1316no—
445C22×C4—138no—
446C22×C4—134no—
447C22×C4—134no—
448C22×C4—132no—
449C22×C4—132no—
450C22×C4—132no—
451C22×C4—2616no—
452C22×C4—2632no—
453C22×C4—2632no—
454C22×C4—268no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—268no—
459C22×C4—262no—
460C22×C4—264no—
461C22×C4—268no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—264no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4C23×D1312yes—
469C22×C4C23×D1314yes—
470C22×C4C23×D1312yes—
471C22×C4C23×D1314yes—
472C4⋊C4—2616no—
473C4⋊C4—2616no—
474C4⋊C4—2616no—
475C4⋊C4—2616no—
476C4⋊C4—268no—
477C4⋊C4—268no—
478C4⋊C4—2616no—
479C22⋊C4—28no—
480C22⋊C4—28no—
481C22⋊C4—1316no—
482C22⋊C4—268no—
483C22⋊C4—268no—
484C22⋊C4—2616no—
485C22⋊C4—2616no—
486C42—2616no—
487C13C2×#241311yescharacteristic, complemented, Sylow
488C23—216no—
489C23—28no—
490C23—216no—
491C23—28no—
492C23—24no—
493C23—24no—
494C23—262no—
495C23—262no—
496C23—262no—
497C23—264no—
498C23—264no—
499C23—524no—
500C23—528no—
501C23—524no—
502C23—528no—
503C23—524no—
504C23#88138116yes—
505C23C2×#612714yes—
506C23C2×#612712yes—
507C23C2×D4×D1314yes—
508C23C2×D4×D1314yes—
509C23C2×D4×D1312yes—
510C23C2×D4×D1312yes—
511C23#41×D1314yes—
512C23#8825714yes—
513C23C24×D1311yescharacteristic
514D4—5216no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—416no—
526C2×C4—48no—
527C2×C4—44no—
528C2×C4—48no—
529C2×C4—44no—
530C2×C4—138no—
531C2×C4—134no—
532C2×C4—134no—
533C2×C4—138no—
534C2×C4—2632no—
535C2×C4—2632no—
536C2×C4—268no—
537C2×C4—268no—
538C2×C4—2616no—
539C2×C4—2616no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—264no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—524no—
552C22—232no—
553C22—28no—
554C22—24no—
555C22—28no—
556C22—24no—
557C22—524no—
558C22—522no—
559C22—522no—
560C22—524no—
561C22—522no—
562C22—1048no—
563C22C2×#8813818yes—
564C22C2×#8813814yes—
565C22#1171923618yes—
566C22#1171935314yes—
567C22#1171936018yes—
568C22#1171936114yes—
569C22C22×#612711yescharacteristic
570C22C22×D4×D1311yescharacteristic
571C22C22×D4×D1311yescharacteristic
572C22C2×#41×D1312yes—
573C22C2×#8825712yes—
574C4—44no—
575C4—44no—
576C4—42no—
577C4—42no—
578C4—268no—
579C4—264no—
580C4—264no—
581C4—268no—
582C4—522no—
583C2—28no—
584C2—1042no—
585C2#1311824518yesdirect product factor
586C2C22×#8813811yescharacteristic
587C2C2×#1171936111yescharacteristic
588C2C2×#1171935311yescharacteristic
589C2C2×#1171936012yes—
590C2C2×#1171923612yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#381C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#381D13
hypocenterC13C2×#2413
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. C22×#88131C2semidirect
4. C23×#6101C2semidirect
5. #13118245C2direct (N × H)
6. C2×#11718318C2semidirect
7. C2×#11718337C2semidirect
8. C2×#11718308C2semidirect
9. C2×#11718330C2semidirect
11. C2×#11718607C2semidirect
12. C2×C13×#381C2semidirect
34. C22×#6101C22semidirect
39. C2×#88131C22semidirect
40. C13×#381C22semidirect
46. #11718607C22semidirect
47. #11718337C22semidirect
48. #11718330C22semidirect
49. #11718318C22semidirect
50. #11718308C22semidirect
204. C2×#381D13semidirect
302. #381C2×D13semidirect
403. C2×C13#2413semidirect
487. C13C2×#2413semidirect
585. C2#13118245direct (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×#881312
C23×#61012
#131182452
C2×#117183182
C2×#117183372
C2×#117183082
C2×#117183302
C2×#117186192
C2×#117186072
C2×C13×#3812
C2×#241313