Finite Group Databasebeta

← C2×#13126060 #16735044

Subgroups — C2×#13126060 #16735044

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C2×#11719329C211yesmaximal, characteristic
3#13126060C2116yesmaximal, direct product factor
4C2×#11718517C212yesmaximal, complemented
5C2×#11718456C212yesmaximal, complemented
6C2×#11718704C211yesmaximal, characteristic, complemented
7C2×#11718397C211yesmaximal, characteristic
8C2×#11718628C211yesmaximal, characteristic
9C2×#11718455C212yesmaximal, complemented
10C2×#11718531C212yesmaximal, complemented
11C2×#11718380C211yesmaximal, characteristic, complemented
12C2×C13×#483C211yesmaximal, characteristic, complemented
13C23×Dic26—21no—
14C2×C13×C22⋊Q8C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C2×#88201C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6101—21no—
21C22×C4×Dic13C2211yescharacteristic
22#11719329—24no—
23#11719329C2218yes—
24C2×#88152—21no—
25C2×#88147C2211yescharacteristic
26C2×#88146—21no—
27C2×#88144C2211yescharacteristic
28C2×#88142—24no—
29C2×#88142—21no—
30C2×#88142—21no—
31C2×#88142C2212yes—
32C2×#88142C2212yes—
33C2×#88142C2218yescomplemented
34C2×#88140—21no—
35C2×#88135—21no—
36C13×#483C2218yescomplemented
37C2×C13×#106C2212yes—
38C2×C13×#103C2212yes—
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×#88075C2212yes—
41C2×C22⋊#1055C2211yescharacteristic
42C2×#88061C2212yes—
43C2×#88058C2212yes—
44C2×#88055C2212yes—
45C2×#88054C2212yes—
46#11718704C2218yescomplemented
47#11718628C2218yes—
48C2×#88049C2212yes—
49C2×#88048C2212yes—
50C2×#88047C2212yes—
51#11718531C22116yescomplemented
52#11718517C22116yescomplemented
53#11718456C22116yescomplemented
54#11718455C22116yescomplemented
55#11718397C2218yes—
56#11718380C2218yescomplemented
57C22×Q8×C13C2311yescharacteristic
58C23×C4×C13—21no—
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C23×Dic13—21no—
62C23×Dic13D411yescharacteristic
63C23×Dic13D411yescharacteristic
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C22×Dic26—22no—
67C22×Dic26—22no—
68C22×Dic26—28no—
69C22×Dic26—48no—
70C22×C8×C13C2312yes—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8C2314yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2314yes—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80#88201—22no—
81#88201C2314yes—
82Q8×Dic13—22no—
83Q8×Dic13C2314yes—
84#88184—22no—
85#88184C2314yes—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2312yes—
95C2×C4⋊Dic13C2314yes—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—28no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13D414yes—
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2314yes—
108C22×#1055C2312yes—
109#88152—28no—
110#88147—22no—
111#88147C2314yes—
112#88146—28no—
113#88144—22no—
114#88144C2314yes—
115#88142—24no—
116#88142—24no—
117#88142—28no—
118#88142—28no—
119#88142C2318yes—
120#88142C2318yes—
121#88140—28no—
122#88135—28no—
123C13×#106C2318yes—
124C13×#103C2318yes—
125C13×C22⋊C8C2314yes—
126#88075C2318yes—
127C22⋊#1055C2314yes—
128#88061C2318yes—
129#88058C2318yes—
130#88055C2318yes—
131#88054C2318yes—
132#88049C2318yes—
133#88048C2318yes—
134#88047C2318yes—
135C2×#3238—131nomaximal, Sylow
136C24×C13C2×D411yescharacteristic
137C23×D13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—24no—
140C2×Q8×C13C2412yes—
141C22×C4×C13—24no—
142C22×C4×C13—21no—
143C22×C4×C13—24no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—44no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2411yescharacteristic
151C2×C22⋊D13—24no—
152C2×C22⋊D13—44no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—21no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—44no—
159C22×Dic13C2×D414yes—
160C22×Dic13C2×D414yes—
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C2×D52—24no—
166C2×D52—21no—
167C2×D52C2412yes—
168C2×C4×D13—24no—
169C2×C4×D13—44no—
170C2×Dic26—28no—
171C2×Dic26—28no—
172C2×Dic26—48no—
173C2×Dic26—48no—
174C2×Dic26—432no—
175C2×C8×C13—24no—
176C2×C8×C13C2414yes—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4C2414yes—
182C13×C4⋊C4C2412yes—
183C13×C22⋊C4—24no—
184#6103—24no—
185#6103—24no—
186#6103—24no—
187#6103—24no—
188C4⋊Dic13—24no—
189C4⋊Dic13—22no—
190C4⋊Dic13—21no—
191C4⋊Dic13—24no—
192C4⋊Dic13—24no—
193C4⋊Dic13C2414yes—
194C4⋊Dic13C2412yes—
195#6101—24no—
196#6101—28no—
197#6101—28no—
198C4×Dic13—24no—
199C4×Dic13C2×D412yes—
200C4×Dic13C2×D414yes—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2412yes—
204C4×Dic13C2412yes—
205C2×#1055—24no—
206C2×#1055C2414yes—
207C22×C4⋊Q8—131no—
208C2×#529—131no—
209#3238—1316no—
210C2×#501—132no—
211C2×#489—132no—
212C2×#483—131no—
213C2×#483D1311yescharacteristic, complemented
214C2×#480—131no—
215C2×#480—131no—
216C2×#477—132no—
217C2×#476—132no—
218C2×#432—131no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13AGL(1,ℤ/8)14yes—
222C23×C13C22×D412yes—
223C23×C13C22×D411yescharacteristic
224C22×D13—22no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13—42no—
228Q8×C13—24no—
229Q8×C13—42no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—42no—
237C2×C4×C13—48no—
238C2×C4×C13—44no—
239C2×C4×C13—42no—
240C2×C4×C13C22×D412yes—
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C132−1+414yes—
243C2×C4×C13C2511yescharacteristic
244C22⋊D13—48no—
245C2×Dic13—28no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—28no—
250C2×Dic13—22no—
251C2×Dic13—24no—
252C2×Dic13—48no—
253C2×Dic13—44no—
254C2×Dic13—42no—
255C2×Dic13#13714yes—
256C2×Dic13C22×D412yes—
257C2×Dic13C22×D412yes—
258C2×Dic13C22×D412yes—
259C2×Dic13C22×D412yes—
260D52—24no—
261D52—42no—
262C4×D13—48no—
263Dic26—416no—
264Dic26—416no—
265C8×C13—24no—
266#1055—24no—
267C23×Q8—261no—
268C2×C4⋊Q8—132no—
269C2×C4⋊Q8—132no—
270C2×C4⋊Q8—138no—
271C2×C4⋊Q8—261no—
272C2×C4⋊Q8—261no—
273C2×C4⋊Q8—264no—
274#529—138no—
275#529—264no—
276C2×#126—261no—
277C2×#125—131no—
278C2×#124—131no—
279C2×#123—261no—
280C2×C22⋊Q8C2×D1311yescharacteristic
281C2×#121—131no—
282C2×C4×Q8—131no—
283C2×C4×D4—131no—
284C2×C4×D4—261no—
285C2×#117—261no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—261no—
288C22×C4⋊C4C2×D1311yescharacteristic
289C22×C42—131no—
290#501—1316no—
291#489—1316no—
292#483—138no—
293#483C2×D1318yescomplemented
294#480—138no—
295#480—138no—
296#477—1316no—
297#476—1316no—
298#432—138no—
299C2×#107—132no—
300C2×#107—132no—
301C2×#106—132no—
302C2×#106C2×D1312yes—
303C2×C4⋊C8—132no—
304C2×#103—132no—
305C2×#103C2×D1312yes—
306C2×#102—132no—
307C2×#102—132no—
308C2×C22⋊C8—131no—
309C2×C22⋊C8C2×D1311yescharacteristic
310C2×#97—132no—
311C22×C13—22no—
312C22×C13—28no—
313C22×C13—22no—
314C22×C13#53612yes—
315C22×C13C2×AGL(1,ℤ/8)14yes—
316C22×C13C2×AGL(1,ℤ/8)12yes—
317C22×C13C2×#13712yes—
318C22×C13C23×D411yescharacteristic
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—42no—
322C2×D13—84no—
323C4×C13—22no—
324C4×C13—42no—
325C4×C13—44no—
326C4×C13—42no—
327C4×C13#53612yes—
328C4×C13C2×2−1+412yes—
329Dic13—22no—
330Dic13—22no—
331Dic13—22no—
332Dic13—44no—
333Dic13—42no—
334Dic13C2×#13714yes—
335C22×Q8—268no—
336C22×Q8—262no—
337C22×Q8—262no—
338C22×Q8—528no—
339C22×Q8C22×D1311yescharacteristic
340C22×D4—131no—
341C22×D4—261no—
342C23×C4—21no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—261no—
346C23×C4—261no—
347C23×C4C22×D1311yescharacteristic
348C22×C8—132no—
349C22×C8C22×D1312yes—
350C4⋊Q8—138no—
351C4⋊Q8—138no—
352C4⋊Q8—268no—
353C4⋊Q8—264no—
354C4⋊Q8—264no—
355C4⋊Q8—268no—
356#126—268no—
357#125—134no—
358#125—262no—
359#124—134no—
360#124—262no—
361#123—268no—
362C22⋊Q8—22no—
363C22⋊Q8C22×D1314yes—
364#121—134no—
365#121—262no—
366C4×Q8—134no—
367C4×Q8—262no—
368C4×D4—134no—
369C4×D4—262no—
370C4×D4—268no—
371#117—268no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—132no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1312yes—
387C2×C4⋊C4C22×D1314yes—
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—134no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—134no—
400C2×C42—261no—
401#107—138no—
402#107—138no—
403#106—138no—
404#106C22×D1318yes—
405C4⋊C8—138no—
406#103—138no—
407#103C22×D1318yes—
408#102—138no—
409#102—138no—
410C22⋊C8—134no—
411C22⋊C8C22×D1314yes—
412#97—138no—
413C2×C13—24no—
414C2×C13#323814yescomplemented
415C2×C13C2×#53611yescharacteristic
416C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
417C2×C13C22×#13711yescharacteristic
418D13—82no—
419C24—261no—
420C24D4×D1311yescharacteristic
421C2×Q8—21no—
422C2×Q8—24no—
423C2×Q8—268no—
424C2×Q8—268no—
425C2×Q8—5232no—
426C2×Q8—528no—
427C2×Q8—528no—
428C2×Q8C23×D1312yes—
429C2×D4—132no—
430C2×D4—264no—
431C2×D4—261no—
432C2×D4—264no—
433C2×D4—524no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—44no—
440C22×C4—131no—
441C22×C4—134no—
442C22×C4—134no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—264no—
449C22×C4—264no—
450C22×C4—261no—
451C22×C4—262no—
452C22×C4—524no—
453C22×C4—524no—
454C22×C4D4×D1312yes—
455C22×C4D4×D1311yescharacteristic
456C22×C4C23×D1312yes—
457C22×C4C23×D1311yescharacteristic
458C2×C8—24no—
459C2×C8—134no—
460C2×C8—264no—
461C2×C8C23×D1314yes—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—134no—
467C4⋊C4—132no—
468C4⋊C4—268no—
469C4⋊C4—268no—
470C4⋊C4—264no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—264no—
474C4⋊C4—262no—
475C4⋊C4—261no—
476C4⋊C4C23×D1314yes—
477C4⋊C4C23×D1312yes—
478C22⋊C4—24no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C22⋊C4—264no—
482C22⋊C4—264no—
483C42—134no—
484C42—132no—
485C42—132no—
486C42—134no—
487C42—132no—
488C42—132no—
489C42—264no—
490C13C2×#323811yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—262no—
494C23—522no—
495C23—522no—
496C23—522no—
497C23#8816814yes—
498C23C2×D4×D1312yes—
499C23C2×D4×D1311yescharacteristic
500Q8—24no—
501Q8—42no—
502Q8—5216no—
503Q8—5216no—
504D4—264no—
505D4—528no—
506D4—522no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—134no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—268no—
523C2×C4—268no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—264no—
529C2×C4—528no—
530C2×C4—528no—
531C2×C4—524no—
532C2×C4—522no—
533C2×C4C2×D4×D1312yes—
534C2×C4C2×D4×D1311yescharacteristic
535C2×C4#8825714yes—
536C2×C4C24×D1311yescharacteristic
537C8—24no—
538C8—264no—
539C22—22no—
540C22—28no—
541C22—22no—
542C22—522no—
543C22—522no—
544C22—522no—
545C22—1044no—
546C22#1171935312yes—
547C22C2×#8816814yes—
548C22C2×#8816812yes—
549C22D13×#13712yes—
550C22C22×D4×D1311yescharacteristic
551C4—22no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—134no—
556C4—262no—
557C4—262no—
558C4—262no—
559C4—524no—
560C4—522no—
561C4#1171935312yes—
562C4C2×#8825712yes—
563C2—24no—
564C2—1042no—
565C2#1312606014yesdirect product factor
566C2C2×#1171935311yescharacteristic
567C2C22×#8816811yescharacteristic
568C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#483C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#483D13
hypocenterC13C2×#3238
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
3. #13126060C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718456C2semidirect
6. C2×#11718704C2semidirect
9. C2×#11718455C2semidirect
10. C2×#11718531C2semidirect
11. C2×#11718380C2semidirect
12. C2×C13×#483C2semidirect
33. C2×#88142C22semidirect
36. C13×#483C22semidirect
46. #11718704C22semidirect
51. #11718531C22semidirect
52. #11718517C22semidirect
53. #11718456C22semidirect
54. #11718455C22semidirect
56. #11718380C22semidirect
213. C2×#483D13semidirect
293. #483C2×D13semidirect
414. C2×C13#3238semidirect
490. C13C2×#3238semidirect
565. C2#13126060direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C2×#117193292
#131260602
C2×#117185172
C2×#117184562
C2×#117187042
C2×#117183972
C2×#117186282
C2×#117184552
C2×#117185312
C2×#117183802
C2×C13×#4832
C2×#323813