Finite Group Databasebeta

← C2×#13126051 #16735072

Subgroups — C2×#13126051 #16735072

Order 3328.

1758 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic
2C2×#11719433C211yesmaximal, characteristic
3#13126051C2116yesmaximal, direct product factor
4C2×#11718741C211yesmaximal, characteristic, complemented
5C2×#11718730C211yesmaximal, characteristic, complemented
6C2×#11718364C211yesmaximal, characteristic, complemented
7C2×#11718528C212yesmaximal
8C2×#11718549C212yesmaximal
9C2×#11718536C212yesmaximal, complemented
10C2×#11718515C212yesmaximal, complemented
11C2×#11718366C211yesmaximal, characteristic
12C2×C13×#501C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C13×#125C2211yescharacteristic
15C2×#88200—21no—
16C2×Q8×Dic13—21no—
17#11719433—24no—
18#11719433C2218yes—
19#11719393—24no—
20#11719393C2218yes—
21C2×#88151C2212yes—
22C2×#88150—21no—
23C2×#88150—21no—
24C2×#88146—21no—
25C2×#88146C2211yescharacteristic
26C2×#88146C2211yescharacteristic
27C2×#88144—21no—
28C2×#88142C2211yescharacteristic
29C2×#88142C2211yescharacteristic
30C2×#88141—21no—
31C2×#88141—21no—
32C2×#88141C2212yes—
33C2×C42×D13C2211yescharacteristic
34C2×#88124C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#501C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×#106C2212yes—
39C2×C13×#97C2211yescharacteristic
40C2×#88060C2212yes—
41C2×#88056C2212yes—
42C2×#88056C2212yes—
43C2×#88054C2212yes—
44#11718741C2218yescomplemented
45#11718730C2218yescomplemented
46C2×#88050C2212yes—
47C2×#88050C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718549C22116yes—
52#11718536C22116yescomplemented
53#11718528C22116yes—
54#11718515C22116yescomplemented
55#11718366C2218yes—
56#11718364C2218yescomplemented
57C22×Q8×C13—21no—
58C22×C4×D13D411yescharacteristic
59C22×C4×D13D411yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×Dic26—21no—
62C22×Dic26—21no—
63C22×Dic26C2312yes—
64C22×C8×C13C2312yes—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8C2314yes—
67C13×#125—22no—
68C13×#125C2314yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76#88200—28no—
77Q8×Dic13—28no—
78C2×#6103—22no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—22no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2312yes—
98#88151—24no—
99#88151C2318yes—
100#88150—28no—
101#88150—28no—
102#88146—28no—
103#88146—22no—
104#88146—22no—
105#88146C2314yes—
106#88146C2314yes—
107#88144—28no—
108#88142—22no—
109#88142—22no—
110#88142C2314yes—
111#88142C2314yes—
112#88141—24no—
113#88141—28no—
114#88141—28no—
115#88141C2318yes—
116C42×D13D414yes—
117C42×D13C2314yes—
118#88124—22no—
119#88124C2314yes—
120#88123—22no—
121#88123C2314yes—
122C13×#107C2318yes—
123C13×#106C2318yes—
124C13×#97C2314yes—
125#88060C2318yes—
126#88056C2318yes—
127#88056C2318yes—
128#88054C2318yes—
129#88050C2318yes—
130#88050C2318yes—
131#88048C2318yes—
132#88047C2318yes—
133#88043C2314yes—
134C2×#3237—131nomaximal, Sylow
135C23×D13C2×D411yescharacteristic
136C2×Q8×C13—24no—
137C2×Q8×C13—44no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C2×C4×D13—24no—
151C2×C4×D13—24no—
152C2×C4×D13—42no—
153C2×C4×D13C2×D412yes—
154C2×C4×D13C2×D414yes—
155C2×C4×D13C2×D414yes—
156C2×C4×D13C2412yes—
157C2×Dic26—28no—
158C2×Dic26—22no—
159C2×Dic26—24no—
160C2×Dic26—24no—
161C2×Dic26—44no—
162C2×Dic26—44no—
163C2×Dic26C2414yes—
164C2×C8×C13—24no—
165C2×C8×C13C2414yes—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—24no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4C2412yes—
173C13×C4⋊C4C2414yes—
174C13×C4⋊C4C2412yes—
175C42×C13C2×D412yes—
176C42×C13C2412yes—
177#6103—28no—
178#6103—24no—
179#6103—24no—
180C4⋊Dic13—24no—
181C4⋊Dic13—24no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—28no—
185C4⋊Dic13C2412yes—
186C4⋊Dic13C2412yes—
187#6101—24no—
188#6101—24no—
189#6101—24no—
190#6101—24no—
191#6101—28no—
192C4×Dic13—24no—
193C4×Dic13—24no—
194C4×Dic13—28no—
195C4×Dic13C2×D412yes—
196C4×Dic13C2×D414yes—
197C4×Dic13C2×D414yes—
198C4×Dic13C2412yes—
199C2×#1055—24no—
200C2×#1055C2414yes—
201C2×#533—131no—
202C2×#533—131no—
203#3237—1316no—
204C2×#501—131no—
205C2×#501D1311yescharacteristic, complemented
206C2×#491—131no—
207C2×#491—131no—
208C2×#485—132no—
209C2×#485—132no—
210C2×#477—132no—
211C2×#475—132no—
212C2×#432—131no—
213C23×C13C22×D411yescharacteristic
214C22×D13—22no—
215C22×D13—22no—
216C22×D13—22no—
217C22×D13C22×D412yes—
218Q8×C13—48no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—44no—
227C2×C4×C13C22×D412yes—
228C2×C4×C13C22×D412yes—
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C132−1+414yes—
231C2×C4×C13C2511yescharacteristic
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—44no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13#13714yes—
241C2×Dic13C22×D412yes—
242C2×Dic13C22×D412yes—
243C2×Dic13C22×D412yes—
244C4×D13—24no—
245C4×D13—24no—
246C4×D13—28no—
247C4×D13—44no—
248Dic26—28no—
249Dic26—48no—
250Dic26—44no—
251Dic26—48no—
252C8×C13—24no—
253#1055—24no—
254#533—138no—
255#533—138no—
256#533—264no—
257#533—264no—
258C2×C4⋊Q8—131no—
259C2×C4⋊Q8—131no—
260C2×C4⋊Q8—131no—
261C2×C4⋊Q8C2×D1311yescharacteristic
262C2×#125—131no—
263C2×#125—261no—
264C2×#125C2×D1311yescharacteristic
265C2×C22⋊Q8—132no—
266C2×C22⋊Q8—261no—
267C2×C22⋊Q8—261no—
268C2×C22⋊Q8—261no—
269C2×C4×Q8—132no—
270C2×C4×Q8—261no—
271C2×C4×Q8—261no—
272C2×C4×Q8—261no—
273C2×#117—131no—
274C2×#117—131no—
275C2×#117—261no—
276C22×C42—131no—
277#501—138no—
278#501C2×D1318yescomplemented
279#491—138no—
280#491—138no—
281#485—1316no—
282#485—1316no—
283#477—1316no—
284#475—1316no—
285#432—138no—
286C2×#107—132no—
287C2×#107C2×D1312yes—
288C2×#106—132no—
289C2×#106C2×D1312yes—
290C2×C4⋊C8—132no—
291C2×#103—132no—
292C2×#103—132no—
293C2×#103—132no—
294C2×#103—132no—
295C2×C22⋊C8—132no—
296C2×#97—131no—
297C2×#97C2×D1311yescharacteristic
298C22×C13#53612yes—
299C22×C13C2×#13712yes—
300C22×C13#57512yes—
301C22×C13C23×D411yescharacteristic
302C2×D13—22no—
303C2×D13—22no—
304C2×D13—22no—
305C2×D13—44no—
306C4×C13—22no—
307C4×C13—22no—
308C4×C13—42no—
309C4×C13—42no—
310C4×C13—44no—
311C4×C13#53612yes—
312C4×C13C2×2−1+412yes—
313Dic13—22no—
314Dic13—22no—
315Dic13—44no—
316Dic13—42no—
317Dic13—42no—
318Dic13C2×#13714yes—
319C22×Q8—21no—
320C22×Q8—132no—
321C22×Q8—261no—
322C22×Q8—261no—
323C23×C4—131no—
324C23×C4—131no—
325C23×C4—131no—
326C22×C8—132no—
327C22×C8C22×D1312yes—
328C4⋊Q8—22no—
329C4⋊Q8—134no—
330C4⋊Q8—134no—
331C4⋊Q8—134no—
332C4⋊Q8—262no—
333C4⋊Q8—262no—
334C4⋊Q8—262no—
335C4⋊Q8C22×D1314yes—
336#125—22no—
337#125—134no—
338#125—268no—
339#125—262no—
340#125C22×D1314yes—
341C22⋊Q8—138no—
342C22⋊Q8—264no—
343C22⋊Q8—268no—
344C22⋊Q8—268no—
345C22⋊Q8—268no—
346C4×Q8—138no—
347C4×Q8—264no—
348C4×Q8—268no—
349C4×Q8—268no—
350C4×Q8—268no—
351#117—134no—
352#117—134no—
353#117—262no—
354#117—262no—
355#117—268no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1312yes—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—262no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—134no—
379C2×C42—134no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42—262no—
383C2×C42C22×D1311yescharacteristic
384#107—138no—
385#107C22×D1318yes—
386#106—138no—
387#106C22×D1318yes—
388C4⋊C8—138no—
389#103—138no—
390#103—138no—
391#103—138no—
392#103—138no—
393C22⋊C8—138no—
394#97—134no—
395#97C22×D1314yes—
396C2×C13#323714yescomplemented
397C2×C13C2×#53611yescharacteristic
398C2×C13C22×#13711yescharacteristic
399C2×C13C2×#57511yescharacteristic
400D13—42no—
401C24—131no—
402C2×Q8—24no—
403C2×Q8—44no—
404C2×Q8—134no—
405C2×Q8—264no—
406C2×Q8—264no—
407C2×Q8—262no—
408C2×Q8—268no—
409C2×Q8—524no—
410C2×Q8—524no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—131no—
415C22×C4—131no—
416C22×C4—131no—
417C22×C4—134no—
418C22×C4—132no—
419C22×C4—132no—
420C22×C4—134no—
421C22×C4—264no—
422C22×C4—264no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—262no—
426C22×C4—522no—
427C22×C4D4×D1311yescharacteristic
428C22×C4D4×D1311yescharacteristic
429C22×C4C23×D1311yescharacteristic
430C2×C8—24no—
431C2×C8—134no—
432C2×C8—264no—
433C2×C8C23×D1314yes—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—132no—
441C4⋊C4—132no—
442C4⋊C4—268no—
443C4⋊C4—268no—
444C4⋊C4—264no—
445C4⋊C4—264no—
446C4⋊C4—261no—
447C4⋊C4—261no—
448C4⋊C4—264no—
449C4⋊C4—264no—
450C4⋊C4—264no—
451C4⋊C4—264no—
452C4⋊C4C23×D1312yes—
453C4⋊C4C23×D1312yes—
454C4⋊C4C23×D1314yes—
455C22⋊C4—264no—
456C22⋊C4—264no—
457C22⋊C4—268no—
458C42—134no—
459C42—134no—
460C42—132no—
461C42—132no—
462C42—264no—
463C42—264no—
464C42—268no—
465C42D4×D1312yes—
466C42C23×D1312yes—
467C13C2×#323711yescharacteristic, complemented, Sylow
468C23—132no—
469C23—262no—
470C23—262no—
471C23—262no—
472C23C2×D4×D1311yescharacteristic
473Q8—48no—
474Q8—268no—
475Q8—528no—
476Q8—528no—
477Q8—524no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—134no—
487C2×C4—132no—
488C2×C4—132no—
489C2×C4—132no—
490C2×C4—268no—
491C2×C4—262no—
492C2×C4—262no—
493C2×C4—264no—
494C2×C4—264no—
495C2×C4—262no—
496C2×C4—262no—
497C2×C4—264no—
498C2×C4—524no—
499C2×C4—524no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4C2×D4×D1312yes—
503C2×C4C2×D4×D1312yes—
504C2×C4C2×D4×D1311yescharacteristic
505C2×C4#8825414yes—
506C2×C4C24×D1311yescharacteristic
507C8—24no—
508C8—264no—
509C22—262no—
510C22—262no—
511C22—262no—
512C22—524no—
513C22#1171942912yes—
514C22#1171947812yes—
515C22D13×#13712yes—
516C22C22×D4×D1311yescharacteristic
517C4—22no—
518C4—22no—
519C4—42no—
520C4—44no—
521C4—42no—
522C4—134no—
523C4—262no—
524C4—262no—
525C4—522no—
526C4—522no—
527C4—524no—
528C4#1171942912yes—
529C4C2×#8825412yes—
530C2—522no—
531C2#1312605114yesdirect product factor
532C2C2×#1171942911yescharacteristic
533C2C2×D13×#13711yescharacteristic
534C2C2×#1171947811yescharacteristic
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×#3237
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. #13126051C2direct (N × H)
4. C2×#11718741C2semidirect
5. C2×#11718730C2semidirect
6. C2×#11718364C2semidirect
9. C2×#11718536C2semidirect
10. C2×#11718515C2semidirect
12. C2×C13×#501C2semidirect
36. C13×#501C22semidirect
44. #11718741C22semidirect
45. #11718730C22semidirect
52. #11718536C22semidirect
54. #11718515C22semidirect
56. #11718364C22semidirect
205. C2×#501D13semidirect
278. #501C2×D13semidirect
396. C2×C13#3237semidirect
467. C13C2×#3237semidirect
531. C2#13126051direct (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×#117194332
#131260512
C2×#117187412
C2×#117187302
C2×#117183642
C2×#117185282
C2×#117185492
C2×#117185362
C2×#117185152
C2×#117183662
C2×C13×#5012
C2×#323713