Finite Group Databasebeta

← C2×#13126003 #16734948

Subgroups — C2×#13126003 #16734948

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719305C211yesmaximal, characteristic
2C22×#88144C211yesmaximal, characteristic, complemented
3#13126003C2116yesmaximal, direct product factor
4C2×#11718519C212yesmaximal, complemented
5C2×#11718429C212yesmaximal, complemented
6C2×#11718631C211yesmaximal, characteristic, complemented
7C2×#11718382C211yesmaximal, characteristic, complemented
8C2×#11718694C211yesmaximal, characteristic
9C2×#11718518C212yesmaximal, complemented
10C2×#11718424C212yesmaximal, complemented
11C2×#11718379C211yesmaximal, characteristic, complemented
12C2×C13×#481C211yesmaximal, characteristic
13C2×C13×#121C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×#88190C2211yescharacteristic
16C2×#88189—21no—
17C2×D4×Dic13—21no—
18C2×D4×Dic13C2211yescharacteristic
19C22×C4⋊Dic13—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22C22×#6101—21no—
23C22×C4×Dic13C2211yescharacteristic
24#11719305—24no—
25#11719305C2218yes—
26C2×#88144—24no—
27C2×#88144—21no—
28C2×#88144—21no—
29C2×#88144C2212yes—
30C2×#88144C2212yes—
31C2×#88144C2211yescharacteristic
32C2×#88144C2218yescomplemented
33C2×#88141C2211yescharacteristic
34C2×#88133—21no—
35C2×#88131—21no—
36C13×#481C2218yes—
37C2×C13×#106C2212yes—
38C2×C13×#102C2212yes—
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×#88072C2212yes—
41C2×C22⋊#1055C2211yescharacteristic
42C2×#88057C2212yes—
43C2×#88056C2212yes—
44C2×#88054C2212yes—
45C2×C8×Dic13C2212yes—
46#11718694C2218yes—
47#11718631C2218yescomplemented
48C2×#88050C2212yes—
49C2×#88047C2212yes—
50C2×#88047C2212yes—
51#11718519C22116yescomplemented
52#11718518C22116yescomplemented
53#11718429C22116yescomplemented
54#11718424C22116yescomplemented
55#11718382C2218yescomplemented
56#11718379C2218yescomplemented
57C22×D4×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C23×Dic13—21no—
63C23×Dic13D411yescharacteristic
64C23×Dic13D411yescharacteristic
65C22×Dic26C2311yescharacteristic
66C22×C8×C13C2312yes—
67C13×#121—22no—
68C13×#121C2314yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C22⋊C4—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79#88190—22no—
80#88190C2314yes—
81#88189—28no—
82D4×Dic13—28no—
83D4×Dic13—22no—
84D4×Dic13C2314yes—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—28no—
91C2×C4⋊Dic13C2312yes—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2314yes—
94#88178—22no—
95#88178C2314yes—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—28no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13D411yescharacteristic
105C2×C4×Dic13D414yes—
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2314yes—
109C22×#1055C2312yes—
110#88144—24no—
111#88144—24no—
112#88144—28no—
113#88144—28no—
114#88144—22no—
115#88144C2318yes—
116#88144C2318yes—
117#88144C2314yes—
118#88141—22no—
119#88141C2314yes—
120#88133—28no—
121#88131—28no—
122C13×#106C2318yes—
123C13×#102C2318yes—
124C13×C22⋊C8C2314yes—
125#88072C2318yes—
126C22⋊#1055C2314yes—
127#88057C2318yes—
128#88056C2318yes—
129#88054C2318yes—
130C8×Dic13C2318yes—
131#88050C2318yes—
132#88047C2318yes—
133#88047C2318yes—
134C2×#3232—131nomaximal, Sylow
135C24×C13—21no—
136C24×C13C2×D411yescharacteristic
137C2×D4×C13—24no—
138C2×D4×C13—21no—
139C2×D4×C13—24no—
140C2×D4×C13—44no—
141C2×D4×C13C2412yes—
142C22×C4×C13—24no—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—22no—
146C22×C4×C13—44no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—24no—
152C22×Dic13—21no—
153C22×Dic13—24no—
154C22×Dic13—22no—
155C22×Dic13—21no—
156C22×Dic13—24no—
157C22×Dic13—42no—
158C22×Dic13—44no—
159C22×Dic13—44no—
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D414yes—
166C2×Dic26—24no—
167C2×Dic26—21no—
168C2×Dic26C2412yes—
169C2×C8×C13—24no—
170C2×C8×C13C2414yes—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4C2414yes—
175C13×C4⋊C4C2412yes—
176C13×C22⋊C4—24no—
177C22⋊Dic13—24no—
178C22⋊Dic13—24no—
179C22⋊Dic13—24no—
180C22⋊Dic13—24no—
181C4⋊Dic13—24no—
182C4⋊Dic13—22no—
183C4⋊Dic13—21no—
184C4⋊Dic13—24no—
185C4⋊Dic13—28no—
186C4⋊Dic13—28no—
187C4⋊Dic13C2414yes—
188C4⋊Dic13C2412yes—
189#6101—24no—
190#6101—24no—
191#6101—24no—
192#6101—28no—
193#6101—28no—
194C4×Dic13—24no—
195C4×Dic13C2×D414yes—
196C4×Dic13C2×D414yes—
197C4×Dic13C2×D412yes—
198C4×Dic13C2×D412yes—
199C4×Dic13C2412yes—
200C4×Dic13C2412yes—
201C2×#1055—24no—
202C2×#1055C2414yes—
203C2×#529—131no—
204C22×#125—131no—
205#3232—1316no—
206C2×#499—132no—
207C2×#488—132no—
208C2×#484—131no—
209C2×#481D1311yescharacteristic
210C2×#483—131no—
211C2×#480—131no—
212C2×#479—132no—
213C2×#478—132no—
214C2×#431—131no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13#13514yes—
222C23×C13C22×D412yes—
223C23×C13C22×D411yescharacteristic
224D4×C13—24no—
225D4×C13—48no—
226D4×C13—42no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—48no—
233C2×C4×C13—42no—
234C2×C4×C13—44no—
235C2×C4×C13C22×D412yes—
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C132−1+414yes—
238C2×C4×C13C2511yescharacteristic
239C2×Dic13—28no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—22no—
247C2×Dic13—44no—
248C2×Dic13—48no—
249C2×Dic13—42no—
250C2×Dic13—48no—
251C2×Dic13—44no—
252C2×Dic13—42no—
253C2×Dic13C22×D412yes—
254C2×Dic13C22×D412yes—
255C2×Dic13C22×D412yes—
256C2×Dic13C22×D412yes—
257Dic26—24no—
258Dic26—42no—
259C8×C13—24no—
260#1055—24no—
261#529—138no—
262#529—264no—
263C2×#126—261no—
264C2×#125—132no—
265C2×#125—132no—
266C2×#125—131no—
267C2×#125—138no—
268C2×#125—261no—
269C2×#125—261no—
270C2×#125—264no—
271C2×#124—131no—
272C2×#123—261no—
273C2×C22⋊Q8—131no—
274C2×#121C2×D1311yescharacteristic
275C2×C4×Q8—131no—
276C2×C4×D4—131no—
277C2×C4×D4—261no—
278C2×#117—261no—
279C22×C4⋊C4—131no—
280C22×C4⋊C4—261no—
281C22×C4⋊C4—261no—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C42—131no—
284#499—1316no—
285#488—1316no—
286#484—138no—
287#483—138no—
288#481C2×D1318yes—
289#480—138no—
290#479—1316no—
291#478—1316no—
292#431—138no—
293C2×#107—132no—
294C2×#107—132no—
295C2×#106—132no—
296C2×#106C2×D1312yes—
297C2×C4⋊C8—132no—
298C2×#103—132no—
299C2×#103—132no—
300C2×#102—132no—
301C2×#102C2×D1312yes—
302C2×C22⋊C8—131no—
303C2×C22⋊C8C2×D1311yescharacteristic
304C2×C4×C8—132no—
305C22×C13—22no—
306C22×C13—28no—
307C22×C13—22no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—84no—
312C22×C13#53612yes—
313C22×C13C2×#13514yes—
314C22×C13C2×#13512yes—
315C22×C13#57512yes—
316C22×C13C23×D411yescharacteristic
317C4×C13—22no—
318C4×C13—42no—
319C4×C13—44no—
320C4×C13#53612yes—
321C4×C13C2×2−1+412yes—
322Dic13—22no—
323Dic13—22no—
324Dic13—22no—
325Dic13—22no—
326Dic13—42no—
327Dic13—44no—
328Dic13—42no—
329C22×Q8—131no—
330C22×D4—21no—
331C22×D4C22×D1311yescharacteristic
332C23×C4—21no—
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—261no—
336C23×C4—261no—
337C23×C4C22×D1311yescharacteristic
338C22×C8—132no—
339C22×C8C22×D1312yes—
340#126—268no—
341#125—138no—
342#125—138no—
343#125—134no—
344#125—268no—
345#125—264no—
346#125—264no—
347#125—268no—
348#125—262no—
349#124—134no—
350#124—262no—
351#123—268no—
352C22⋊Q8—134no—
353C22⋊Q8—262no—
354#121—22no—
355#121C22×D1314yes—
356C4×Q8—134no—
357C4×Q8—262no—
358C4×D4—134no—
359C4×D4—262no—
360C4×D4—268no—
361#117—268no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4—134no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—268no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—268no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1312yes—
380C2×C4⋊C4C22×D1314yes—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—134no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—134no—
393C2×C42—261no—
394#107—138no—
395#107—138no—
396#106—138no—
397#106C22×D1318yes—
398C4⋊C8—138no—
399#103—138no—
400#103—138no—
401#102—138no—
402#102C22×D1318yes—
403C22⋊C8—134no—
404C22⋊C8C22×D1314yes—
405C4×C8—138no—
406C2×C13—24no—
407C2×C13—82no—
408C2×C13#323214yescomplemented
409C2×C13C2×#53611yescharacteristic
410C2×C13C22×#13511yescharacteristic
411C2×C13C2×#57511yescharacteristic
412C24—21no—
413C24D4×D1311yescharacteristic
414C2×Q8—132no—
415C2×Q8—261no—
416C2×Q8—264no—
417C2×D4—24no—
418C2×D4—21no—
419C2×D4—24no—
420C2×D4—44no—
421C2×D4C23×D1312yes—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—44no—
427C22×C4—134no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—134no—
433C22×C4—264no—
434C22×C4—264no—
435C22×C4—264no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—522no—
440C22×C4—524no—
441C22×C4—524no—
442C22×C4D4×D1312yes—
443C22×C4D4×D1311yescharacteristic
444C22×C4C23×D1312yes—
445C22×C4C23×D1311yescharacteristic
446C2×C8—24no—
447C2×C8—134no—
448C2×C8—264no—
449C2×C8C23×D1314yes—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—134no—
454C4⋊C4—132no—
455C4⋊C4—268no—
456C4⋊C4—268no—
457C4⋊C4—268no—
458C4⋊C4—268no—
459C4⋊C4—264no—
460C4⋊C4—264no—
461C4⋊C4—264no—
462C4⋊C4—264no—
463C4⋊C4—262no—
464C4⋊C4—261no—
465C4⋊C4—264no—
466C4⋊C4C23×D1314yes—
467C4⋊C4C23×D1312yes—
468C22⋊C4—24no—
469C22⋊C4—264no—
470C22⋊C4—264no—
471C22⋊C4—264no—
472C22⋊C4—264no—
473C42—134no—
474C42—132no—
475C42—132no—
476C42—134no—
477C42—132no—
478C42—132no—
479C42—264no—
480C13C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#8817014yes—
488C23C2×D4×D1312yes—
489C23C2×D4×D1311yescharacteristic
490Q8—264no—
491Q8—522no—
492D4—24no—
493D4—48no—
494D4—42no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—132no—
504C2×C4—132no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—268no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—264no—
515C2×C4—524no—
516C2×C4—528no—
517C2×C4—528no—
518C2×C4—524no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4C2×D4×D1312yes—
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4#8825714yes—
524C2×C4C24×D1311yescharacteristic
525C8—24no—
526C8—264no—
527C22—22no—
528C22—28no—
529C22—22no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22#1171935312yes—
535C22C2×#8817014yes—
536C22C2×#8817012yes—
537C22#1171947812yes—
538C22C22×D4×D1311yescharacteristic
539C4—22no—
540C4—42no—
541C4—44no—
542C4—262no—
543C4—262no—
544C4—262no—
545C4—262no—
546C4—524no—
547C4—522no—
548C4—522no—
549C4#1171935312yes—
550C4C2×#8825712yes—
551C2—24no—
552C2—82no—
553C2#1312600314yesdirect product factor
554C2C2×#1171935311yescharacteristic
555C2C22×#8817011yescharacteristic
556C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#481C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#481D13
hypocenterC13C2×#3232
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×#88144C2semidirect
3. #13126003C2direct (N × H)
4. C2×#11718519C2semidirect
5. C2×#11718429C2semidirect
6. C2×#11718631C2semidirect
7. C2×#11718382C2semidirect
9. C2×#11718518C2semidirect
10. C2×#11718424C2semidirect
11. C2×#11718379C2semidirect
32. C2×#88144C22semidirect
47. #11718631C22semidirect
51. #11718519C22semidirect
52. #11718518C22semidirect
53. #11718429C22semidirect
54. #11718424C22semidirect
55. #11718382C22semidirect
56. #11718379C22semidirect
408. C2×C13#3232semidirect
480. C13C2×#3232semidirect
553. C2#13126003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193052
C22×#881442
#131260032
C2×#117185192
C2×#117184292
C2×#117186312
C2×#117183822
C2×#117186942
C2×#117185182
C2×#117184242
C2×#117183792
C2×C13×#4812
C2×#323213