Finite Group Databasebeta

← C2×#13069781 #14781170

Subgroups — C2×#13069781 #14781170

Order 2816.

2818 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2C2×#10622568C211yesmaximal, characteristic
3C2×#10622568C212yesmaximal
4#13069781C218yesmaximal, direct product factor
5C2×#10622165C212yesmaximal, complemented
6C2×C11×#342C211yesmaximal, characteristic, complemented
7C25×D11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2211yescharacteristic
11C22×C22⋊Dic11C2212yes—
12C22×(C2×D11)⋊C4—22no—
13C22×(C2×D11)⋊C4—24no—
14C2×#66977—22no—
15#10623014—22no—
16#10623014—24no—
17#10623014C2214yescomplemented
18C2×#66931—24no—
19#10622568—22no—
20#10622568—24no—
21#10622568C2214yes—
22#10622568C2218yes—
23C11×#342C2214yescomplemented
24#10622165C2218yescomplemented
25C25×C11C2311yescharacteristic
26C24×D11—21no—
27C24×D11—22no—
28C24×D11—21no—
29C24×D11—22no—
30C24×D11—24no—
31C24×D11—22no—
32C24×D11—48no—
33C24×D11Q814yescomplemented
34C24×D11C2312yes—
35C23×C4×C11—22no—
36C23×C4×C11D412yes—
37C23×Dic11—21no—
38C23×Dic11D414yes—
39C22×Dic22—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4D412yes—
46C2×C11×C22⋊C4C2314yes—
47C2×C11×C22⋊C4C2312yes—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11D414yes—
55C2×C22⋊Dic11C2312yes—
56C2×C22⋊Dic11C2314yes—
57C2×(C2×D11)⋊C4—28no—
58C2×(C2×D11)⋊C4—216no—
59C2×(C2×D11)⋊C4—416no—
60C2×(C2×D11)⋊C4—48no—
61C2×C4⋊Dic11—22no—
62#66977—28no—
63#66977—28no—
64C2×Dic11⋊C4—24no—
65#66931—216no—
66#66931—216no—
67C2×#2029—111nomaximal, Sylow
68C24×C11—44no—
69C24×C11C2×D411yescharacteristic
70C24×C11C2×D412yes—
71C24×C11C2×D411yescharacteristic
72C24×C11C2×D412yes—
73C24×C11C2×Q812yes—
74C24×C11#4114yes—
75C24×C11#4112yes—
76C24×C11C2411yescharacteristic
77C23×D11—28no—
78C23×D11—216no—
79C23×D11—28no—
80C23×D11—24no—
81C23×D11—22no—
82C23×D11—24no—
83C23×D11—28no—
84C23×D11—24no—
85C23×D11—24no—
86C23×D11—22no—
87C23×D11—416no—
88C23×D11—48no—
89C23×D11—416no—
90C23×D11—48no—
91C23×D11—416no—
92C23×D11—432no—
93C23×D11—44no—
94C23×D11—48no—
95C23×D11—41no—
96C23×D11—42no—
97C23×D11—41no—
98C23×D11—42no—
99C23×D11—44no—
100C23×D11—42no—
101C23×D11—44no—
102C23×D11C2×Q814yescomplemented
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—44no—
107C22×C4×C11—48no—
108C22×C4×C11—44no—
109C22×C4×C11C2×D414yes—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—48no—
114C22×Dic11—44no—
115C22×Dic11—42no—
116C22×Dic11C2×D418yes—
117C2×Dic22—28no—
118C2×Dic22—84no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—44no—
124C22⋊Dic11—24no—
125C22⋊Dic11—24no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—42no—
130(C2×D11)⋊C4—416no—
131(C2×D11)⋊C4—432no—
132C4⋊Dic11—28no—
133Dic11⋊C4—216no—
134C2×#543—111no—
135C2×#379—112no—
136C2×#379—111no—
137#2029—118no—
138C2×#342—112no—
139C2×#342D1111yescharacteristic, complemented
140C23×C11—24no—
141C23×C11—28no—
142C23×C11—42no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11—48no—
146C23×C11—44no—
147C23×C11—42no—
148C23×C11#12011yescharacteristic
149C23×C11#12012yes—
150C23×C11#12011yescharacteristic
151C23×C11C22⋊Q814yes—
152C23×C11C22⋊Q814yes—
153C23×C11C22⋊Q812yes—
154C23×C11C22⋊Q812yes—
155C23×C11#12412yes—
156C23×C11#12412yes—
157C23×C11#12414yes—
158C23×C11#12414yes—
159C23×C11C22×D411yescharacteristic
160C23×C11C22×D412yes—
161C23×C11C22×Q811yescharacteristic
162C23×C11C2×#4112yes—
163C23×C11C2×#4111yescharacteristic
164C22×D11—28no—
165C22×D11—216no—
166C22×D11—232no—
167C22×D11—216no—
168C22×D11—28no—
169C22×D11—24no—
170C22×D11—48no—
171C22×D11—432no—
172C22×D11—416no—
173C22×D11—416no—
174C22×D11—48no—
175C22×D11—44no—
176C22×D11—48no—
177C22×D11—48no—
178C22×D11—416no—
179C22×D11—432no—
180C22×D11—416no—
181C22×D11—48no—
182C22×D11—416no—
183C22×D11—416no—
184C22×D11—432no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—44no—
188C22×D11—48no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—48no—
192C2×C4×C11—24no—
193C2×C4×C11—44no—
194C2×C4×C11—44no—
195C2×C4×C11—48no—
196C2×C4×C11—44no—
197C2×C4×C11—82no—
198C2×C4×C11—88no—
199C2×Dic11—28no—
200C2×Dic11—48no—
201C2×Dic11—48no—
202C2×Dic11—44no—
203C2×Dic11—42no—
204C2×Dic11—84no—
205C2×Dic11—84no—
206Dic22—88no—
207C26—111no—
208#543—114no—
209#543—224no—
210#543—222no—
211C2×C22⋊Q8—224no—
212C2×C22⋊Q8—222no—
213C22×C22⋊C4—112no—
214C22×C22⋊C4—111no—
215C22×C22⋊C4—224no—
216C22×C22⋊C4—222no—
217C22×C22⋊C4C2×D1112yes—
218C22×C22⋊C4C2×D1111yescharacteristic
219#379—118no—
220#379—114no—
221#379—224no—
222#379—222no—
223#342—118no—
224#342C2×D1114yescomplemented
225C22×C11—22no—
226C22×C11—24no—
227C22×C11—22no—
228C22×C11—24no—
229C22×C11—28no—
230C22×C11—28no—
231C22×C11—24no—
232C22×C11—24no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—41no—
240C22×C11#39312yes—
241C22×C11#39314yes—
242C22×C11#39312yes—
243C22×C11B(4,𝔽2)14yes—
244C22×C11C2×#12011yescharacteristic
245C22×C11C2×C22⋊Q812yes—
246C22×C11C2×C22⋊Q811yescharacteristic
247C22×C11C2×#12411yescharacteristic
248C22×C11C2×#12412yes—
249C2×D11—216no—
250C2×D11—28no—
251C2×D11—48no—
252C2×D11—416no—
253C2×D11—48no—
254C2×D11—44no—
255C2×D11—416no—
256C2×D11—432no—
257C2×D11—44no—
258C2×D11—48no—
259C2×D11—416no—
260C4×C11—44no—
261C4×C11—84no—
262Dic11—48no—
263Dic11—82no—
264C25—114no—
265C25—112no—
266C25—221no—
267C25—222no—
268C25—221no—
269C25—224no—
270C25—222no—
271C25—222no—
272C25—448no—
273C25C22×D1111yescharacteristic
274C22×Q8—222no—
275C23×C4—22no—
276C23×C4—114no—
277C23×C4—221no—
278C23×C4D4412yes—
279C22⋊Q8—2216no—
280C22⋊Q8—2216no—
281C22⋊Q8—228no—
282C22⋊Q8—228no—
283C2×C4⋊C4—224no—
284C2×C4⋊C4—222no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—114no—
291C2×C22⋊C4—114no—
292C2×C22⋊C4—112no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—224no—
298C2×C22⋊C4—2216no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—228no—
301C2×C22⋊C4—448no—
302C2×C22⋊C4—4416no—
303C2×C22⋊C4D4412yes—
304C2×C22⋊C4C22×D1114yes—
305C2×C22⋊C4C22×D1112yes—
306C2×C11—21no—
307C2×C11—22no—
308C2×C11—22no—
309C2×C11—21no—
310C2×C11—22no—
311C2×C11—24no—
312C2×C11#202914yescomplemented
313C2×C11C2×#39311yescharacteristic
314C2×C11C2×B(4,𝔽2)12yes—
315D11—48no—
316C24—44no—
317C24—114no—
318C24—228no—
319C24—2216no—
320C24—228no—
321C24—224no—
322C24—222no—
323C24—224no—
324C24—228no—
325C24—224no—
326C24—224no—
327C24—222no—
328C24—444no—
329C24—448no—
330C24—4416no—
331C24—448no—
332C24—448no—
333C24—4432no—
334C24—4416no—
335C24—4416no—
336C24—442no—
337C24—442no—
338C24—442no—
339C24—441no—
340C24—441no—
341C24—444no—
342C24—444no—
343C24C2×D4411yescharacteristic
344C24C2×D4411yescharacteristic
345C24#433914yes—
346C24D4×D1112yes—
347C24D4×D1112yes—
348C24#434112yes—
349C24Q8×D1112yes—
350C24C23×D1111yescharacteristic
351C2×Q8—228no—
352C2×Q8—884no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—24no—
356C22×C4—44no—
357C22×C4—48no—
358C22×C4—44no—
359C22×C4—118no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4—448no—
364C22×C4—444no—
365C22×C4—442no—
366C22×C4C2×D4414yes—
367C4⋊C4—2216no—
368C4⋊C4—228no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C22⋊C4—224no—
375C22⋊C4—224no—
376C22⋊C4—224no—
377C22⋊C4—224no—
378C22⋊C4—224no—
379C22⋊C4—4416no—
380C22⋊C4—4432no—
381C22⋊C4—442no—
382C11C2×#202911yescharacteristic, complemented, Sylow
383C23—24no—
384C23—28no—
385C23—42no—
386C23—48no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—42no—
391C23—228no—
392C23—2216no—
393C23—2232no—
394C23—2216no—
395C23—228no—
396C23—224no—
397C23—4432no—
398C23—4416no—
399C23—4416no—
400C23—448no—
401C23—444no—
402C23—448no—
403C23—448no—
404C23—4416no—
405C23—448no—
406C23—4432no—
407C23—4416no—
408C23—4416no—
409C23—448no—
410C23—4416no—
411C23—4432no—
412C23—442no—
413C23—442no—
414C23—444no—
415C23—448no—
416C23—444no—
417C23—444no—
418C23—448no—
419C23#6692812yes—
420C23#6692812yes—
421C23#6693512yes—
422C23#6693511yescharacteristic
423C23#6693511yescharacteristic
424C23#6693814yes—
425C23#6693814yes—
426C23#6694914yes—
427C23#6694914yes—
428C23#6695012yes—
429C23#6695012yes—
430C23C22×D4411yescharacteristic
431C23C2×#433912yes—
432C23C2×D4×D1112yes—
433C23C2×#434111yescharacteristic
434C23C2×Q8×D1111yescharacteristic
435Q8—888no—
436C2×C4—24no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—44no—
441C2×C4—82no—
442C2×C4—88no—
443C2×C4—228no—
444C2×C4—448no—
445C2×C4—448no—
446C2×C4—444no—
447C2×C4—442no—
448C2×C4—884no—
449C2×C4—884no—
450C22—28no—
451C22—24no—
452C22—28no—
453C22—24no—
454C22—22no—
455C22—24no—
456C22—22no—
457C22—24no—
458C22—42no—
459C22—44no—
460C22—44no—
461C22—42no—
462C22—42no—
463C22—41no—
464C22—41no—
465C22—2216no—
466C22—228no—
467C22—4416no—
468C22—448no—
469C22—448no—
470C22—444no—
471C22—4432no—
472C22—4416no—
473C22—444no—
474C22—4416no—
475C22—448no—
476C22#1062228612yes—
477C22#1062228614yes—
478C22#1062228612yes—
479C22#1062235414yes—
480C22C2×#6692811yescharacteristic
481C22C2×#6693511yescharacteristic
482C22C2×#6693812yes—
483C22C2×#6694912yes—
484C22C2×#6695011yescharacteristic
485C4—44no—
486C4—84no—
487C4—448no—
488C4—882no—
489C2—22no—
490C2—21no—
491C2—22no—
492C2—21no—
493C2—24no—
494C2—22no—
495C2—448no—
496C2#1306978114yesdirect product factor
497C2C2×#1062228611yescharacteristic
498C2C2×#1062235412yes—
subgroupG/H
centerC23#66935
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#342C2
socleC23×C11#120
prime radicalC25×D11C22
hypercenterC2×#342D11
hypocenterC11C2×#2029
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
4. #13069781C2direct (N × H)
5. C2×#10622165C2semidirect
6. C2×C11×#342C2semidirect
17. #10623014C22semidirect
23. C11×#342C22semidirect
24. #10622165C22semidirect
33. C24×D11Q8semidirect
102. C23×D11C2×Q8semidirect
139. C2×#342D11semidirect
224. #342C2×D11semidirect
312. C2×C11#2029semidirect
382. C11C2×#2029semidirect
496. C2#13069781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230142
C2×#106225682
#130697812
C2×#106221652
C2×C11×#3422
C2×#202911