Finite Group Databasebeta

← C2×#13125381 #16732567

Subgroups — C2×#13125381 #16732567

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic
2C2×D13×C4⋊Q8C211yesmaximal, characteristic
3#13125381C2116yesmaximal, direct product factor
4C2×#11718726C211yesmaximal, characteristic, complemented
5C2×#11718363C211yesmaximal, characteristic, complemented
6C2×#11718741C211yesmaximal, characteristic, complemented
7C2×#11718535C212yesmaximal, complemented
8C2×#11718516C212yesmaximal, complemented
9C2×#11718542C212yesmaximal
10C2×#11718522C212yesmaximal
11C2×#11718368C211yesmaximal, characteristic
12C2×C13×#501C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×#88198—21no—
17C22×#6094C2212yes—
18D13×C4⋊Q8—24no—
19D13×C4⋊Q8C2218yes—
20#11719393—24no—
21#11719393C2218yes—
22C2×#88150—21no—
23C2×#88150—21no—
24C2×#88146C2211yescharacteristic
25C2×#88146C2211yescharacteristic
26C2×C4⋊C4×D13—21no—
27C2×C4⋊C4×D13C2212yes—
28C2×#88142—21no—
29C2×#88142C2212yes—
30C2×#88142C2211yescharacteristic
31C2×#88142C2211yescharacteristic
32C2×#88141—21no—
33C2×#88141—21no—
34C2×C42×D13C2211yescharacteristic
35C2×#88124C2211yescharacteristic
36C2×#88123C2211yescharacteristic
37C13×#501C2218yescomplemented
38C2×C13×#107C2212yes—
39C2×C13×#106C2212yes—
40C2×C13×#97C2211yescharacteristic
41C2×#88058C2212yes—
42C2×#88057C2212yes—
43C2×C8×Dic13C2212yes—
44#11718741C2218yescomplemented
45#11718726C2218yescomplemented
46C2×#88048C2212yes—
47C2×#88048C2212yes—
48C2×#88047C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718542C22116yes—
52#11718535C22116yescomplemented
53#11718522C22116yes—
54#11718516C22116yescomplemented
55#11718368C2218yes—
56#11718363C2218yescomplemented
57C22×Q8×C13—21no—
58C2×Q8×D13—28no—
59C2×Q8×D13—48no—
60C22×C4×D13—22no—
61C22×C4×D13D411yescharacteristic
62C22×C4×D13D411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×Dic26—21no—
65C22×Dic26—21no—
66C22×Dic26—21no—
67C22×Dic26—22no—
68C22×C8×C13C2312yes—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8C2314yes—
71C13×#125—22no—
72C13×#125C2314yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80#88198—28no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2312yes—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—22no—
92C2×#6101—22no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2312yes—
99C2×#6094Q8116yescomplemented
100C2×#6094C2318yes—
101#88150—28no—
102#88150—28no—
103#88146—22no—
104#88146—22no—
105#88146C2314yes—
106#88146C2314yes—
107C4⋊C4×D13—24no—
108C4⋊C4×D13—28no—
109C4⋊C4×D13C2318yes—
110#88142—24no—
111#88142—28no—
112#88142—22no—
113#88142—22no—
114#88142C2318yes—
115#88142C2314yes—
116#88142C2314yes—
117#88141—28no—
118#88141—28no—
119C42×D13D414yes—
120C42×D13C2314yes—
121#88124—22no—
122#88124C2314yes—
123#88123—22no—
124#88123C2314yes—
125C13×#107C2318yes—
126C13×#106C2318yes—
127C13×#97C2314yes—
128#88058C2318yes—
129#88057C2318yes—
130C8×Dic13C2318yes—
131#88048C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134#88047C2318yes—
135#88043C2314yes—
136C2×#3165—131nomaximal, Sylow
137C23×D13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—44no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152Q8×D13—432no—
153C2×C4×D13—24no—
154C2×C4×D13—24no—
155C2×C4×D13—28no—
156C2×C4×D13—48no—
157C2×C4×D13C2×D414yes—
158C2×C4×D13C2×D414yes—
159C2×C4×D13C2×D412yes—
160C2×C4×D13C2×Q818yes—
161C2×C4×D13C2412yes—
162C2×Dic26—24no—
163C2×Dic26—24no—
164C2×Dic26—24no—
165C2×Dic26—28no—
166C2×Dic26—44no—
167C2×Dic26—44no—
168C2×Dic26—48no—
169C2×Dic26—44no—
170C2×C8×C13C2×Q818yescomplemented
171C2×C8×C13C2414yes—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C2412yes—
179C13×C4⋊C4C2414yes—
180C13×C4⋊C4C2412yes—
181C42×C13C2×D412yes—
182C42×C13C2412yes—
183#6103—24no—
184#6103—24no—
185C4⋊Dic13—22no—
186C4⋊Dic13—24no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C2414yes—
190C4⋊Dic13C2412yes—
191C4⋊Dic13C2412yes—
192#6101—24no—
193#6101—24no—
194#6101—24no—
195#6101—24no—
196#6101—28no—
197#6101—28no—
198C4×Dic13—24no—
199C4×Dic13—24no—
200C4×Dic13C2×D412yes—
201C4×Dic13C2×D414yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2412yes—
204C2×#1055C2×Q818yescomplemented
205C2×#1055C2414yes—
206#6094C2×Q8132yescomplemented
207C2×#533—131no—
208C22×C4⋊Q8—131no—
209#3165—1316no—
210C2×#501—131no—
211C2×#501—131no—
212C2×#501—131no—
213C2×#501D1311yescharacteristic, complemented
214C2×#500—132no—
215C2×#498—132no—
216C2×#428—132no—
217C2×#428—132no—
218C2×C4×M16—131no—
219C23×C13C22×D411yescharacteristic
220C22×D13—22no—
221C22×D13—22no—
222C22×D13C4⋊Q814yes—
223C22×D13C22×D412yes—
224Q8×C13—48no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—44no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13C22×D412yes—
234C2×C4×C13C22×D412yes—
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C22×Q814yes—
237C2×C4×C13C2511yescharacteristic
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—24no—
241C2×Dic13—44no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13C4⋊Q814yes—
245C2×Dic13AGL(1,ℤ/8)14yes—
246C2×Dic13#13714yes—
247C2×Dic13C22×D412yes—
248C2×Dic13C22×D412yes—
249C2×Dic13C22×D412yes—
250C4×D13—28no—
251C4×D13—28no—
252C4×D13—416no—
253C4×D13C4⋊Q818yes—
254C4×D13C22×Q818yes—
255Dic26—48no—
256Dic26—48no—
257Dic26—416no—
258Dic26—48no—
259C8×C13C22×Q818yescomplemented
260#1055C22×Q818yescomplemented
261C23×Q8—261no—
262C22×M16—132no—
263#533—138no—
264#533—264no—
265C2×C4⋊Q8—138no—
266C2×C4⋊Q8—131no—
267C2×C4⋊Q8—132no—
268C2×C4⋊Q8—131no—
269C2×C4⋊Q8—131no—
270C2×C4⋊Q8—261no—
271C2×C4⋊Q8—264no—
272C2×C4⋊Q8—261no—
273C2×C4⋊Q8C2×D1311yescharacteristic
274C2×#125—131no—
275C2×#125C2×D1311yescharacteristic
276C2×C22⋊Q8—261no—
277C2×C22⋊Q8—261no—
278C2×C4×Q8—261no—
279C2×C4×Q8—261no—
280C2×#117—131no—
281C2×#117—131no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—261no—
284C22×C42—131no—
285#501—138no—
286#501—138no—
287#501—138no—
288#501C2×D1318yescomplemented
289#500—1316no—
290#498—1316no—
291#428—1316no—
292#428—1316no—
293C2×#107—132no—
294C2×#107—132no—
295C2×#107—132no—
296C2×#107C2×D1312yes—
297C2×#106—132no—
298C2×#106—132no—
299C2×#106—132no—
300C2×#106C2×D1312yes—
301C4×M16—138no—
302C2×#97—131no—
303C2×#97C2×D1311yescharacteristic
304C2×C4×C8—132no—
305C22×C13C2×C4⋊Q812yes—
306C22×C13C2×AGL(1,ℤ/8)12yes—
307C22×C13C2×#13712yes—
308C22×C13C23×D411yescharacteristic
309C2×D13—28no—
310C2×D13—22no—
311C2×D13—22no—
312C2×D13C2×C4⋊Q814yes—
313C4×C13—22no—
314C4×C13—22no—
315C4×C13—44no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13C2×C4⋊Q812yes—
319C4×C13C23×Q812yes—
320Dic13—44no—
321Dic13—42no—
322Dic13—42no—
323Dic13C2×C4⋊Q814yes—
324Dic13C2×AGL(1,ℤ/8)14yes—
325Dic13C2×#13714yes—
326C22×Q8—21no—
327C22×Q8—261no—
328C22×Q8—261no—
329C22×Q8—262no—
330C22×Q8—268no—
331C22×Q8—261no—
332C22×Q8—528no—
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—131no—
336C23×C4—262no—
337C2×M16—1316no—
338C2×M16—138no—
339C22×C8—132no—
340C22×C8C22×D1312yes—
341C4⋊Q8—22no—
342C4⋊Q8—138no—
343C4⋊Q8—134no—
344C4⋊Q8—134no—
345C4⋊Q8—134no—
346C4⋊Q8—268no—
347C4⋊Q8—264no—
348C4⋊Q8—262no—
349C4⋊Q8—262no—
350C4⋊Q8—268no—
351C4⋊Q8—262no—
352C4⋊Q8C22×D1314yes—
353#125—22no—
354#125—134no—
355#125—262no—
356#125C22×D1314yes—
357C22⋊Q8—268no—
358C22⋊Q8—268no—
359C4×Q8—268no—
360C4×Q8—268no—
361#117—134no—
362#117—134no—
363#117—262no—
364#117—262no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—132no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—264no—
373C2×C4⋊C4—268no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1312yes—
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—134no—
390C2×C42—134no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22×D1311yescharacteristic
394#107—138no—
395#107—138no—
396#107—138no—
397#107C22×D1318yes—
398#106—138no—
399#106—138no—
400#106—138no—
401#106C22×D1318yes—
402#97—134no—
403#97C22×D1314yes—
404C4×C8—138no—
405C2×C13#316514yescomplemented
406C2×C13C22×C4⋊Q811yescharacteristic
407C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
408C2×C13C22×#13711yescharacteristic
409D13—24no—
410C24—131no—
411C2×Q8—24no—
412C2×Q8—44no—
413C2×Q8—264no—
414C2×Q8—264no—
415C2×Q8—268no—
416C2×Q8—264no—
417C2×Q8—524no—
418C2×Q8—528no—
419C2×Q8—524no—
420C2×Q8—524no—
421C2×Q8—5232no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—132no—
429C22×C4—138no—
430C22×C4—132no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—264no—
434C22×C4—264no—
435C22×C4—268no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—528no—
440C22×C4D4×D1311yescharacteristic
441C22×C4D4×D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443M16—1332no—
444C2×C8—138no—
445C2×C8—134no—
446C2×C8Q8×D1318yescomplemented
447C2×C8C23×D1314yes—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—132no—
455C4⋊C4—134no—
456C4⋊C4—132no—
457C4⋊C4—268no—
458C4⋊C4—268no—
459C4⋊C4—264no—
460C4⋊C4—264no—
461C4⋊C4—262no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—264no—
465C4⋊C4—264no—
466C4⋊C4—264no—
467C4⋊C4C23×D1312yes—
468C4⋊C4C23×D1314yes—
469C4⋊C4C23×D1312yes—
470C22⋊C4—264no—
471C22⋊C4—264no—
472C42—134no—
473C42—134no—
474C42—132no—
475C42—132no—
476C42—264no—
477C42—264no—
478C42D4×D1312yes—
479C42C23×D1312yes—
480C13C2×#316511yescharacteristic, complemented, Sylow
481C23—134no—
482C23—132no—
483C23—262no—
484C23—262no—
485C23C2×D4×D1311yescharacteristic
486Q8—48no—
487Q8—528no—
488Q8—528no—
489Q8—528no—
490Q8—5216no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—134no—
500C2×C4—134no—
501C2×C4—134no—
502C2×C4—132no—
503C2×C4—132no—
504C2×C4—132no—
505C2×C4—138no—
506C2×C4—138no—
507C2×C4—268no—
508C2×C4—268no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—264no—
512C2×C4—5216no—
513C2×C4—524no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4C2×D4×D1312yes—
517C2×C4C2×D4×D1312yes—
518C2×C4C2×D4×D1311yescharacteristic
519C2×C4C2×Q8×D1314yes—
520C2×C4C24×D1311yescharacteristic
521C8—138no—
522C8C2×Q8×D1318yescomplemented
523C22—134no—
524C22—268no—
525C22—262no—
526C22—262no—
527C22D13×C4⋊Q812yes—
528C22D13×AGL(1,ℤ/8)12yes—
529C22D13×#13712yes—
530C22C22×D4×D1311yescharacteristic
531C4—22no—
532C4—22no—
533C4—44no—
534C4—42no—
535C4—42no—
536C4—134no—
537C4—134no—
538C4—134no—
539C4—524no—
540C4—522no—
541C4—522no—
542C4D13×C4⋊Q812yes—
543C4C22×Q8×D1312yes—
544C2—264no—
545C2#1312538114yesdirect product factor
546C2C2×D13×C4⋊Q811yescharacteristic
547C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
548C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#501D13
hypocenterC13C2×#3165
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13125381C2direct (N × H)
4. C2×#11718726C2semidirect
5. C2×#11718363C2semidirect
6. C2×#11718741C2semidirect
7. C2×#11718535C2semidirect
8. C2×#11718516C2semidirect
12. C2×C13×#501C2semidirect
37. C13×#501C22semidirect
44. #11718741C22semidirect
45. #11718726C22semidirect
52. #11718535C22semidirect
54. #11718516C22semidirect
56. #11718363C22semidirect
99. C2×#6094Q8semidirect
170. C2×C8×C13C2×Q8semidirect
204. C2×#1055C2×Q8semidirect
206. #6094C2×Q8semidirect
213. C2×#501D13semidirect
259. C8×C13C22×Q8semidirect
260. #1055C22×Q8semidirect
288. #501C2×D13semidirect
405. C2×C13#3165semidirect
446. C2×C8Q8×D13semidirect
480. C13C2×#3165semidirect
522. C8C2×Q8×D13semidirect
545. C2#13125381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193932
C2×D13×C4⋊Q82
#131253812
C2×#117187262
C2×#117183632
C2×#117187412
C2×#117185352
C2×#117185162
C2×#117185422
C2×#117185222
C2×#117183682
C2×C13×#5012
C2×#316513