Finite Group Databasebeta

← C2×#13069780 #14781169

Subgroups — C2×#13069780 #14781169

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×#10622860C212yesmaximal
3#13069780C218yesmaximal, direct product factor
4C2×#10622164C211yesmaximal, characteristic, complemented
5C2×#10622165C212yesmaximal, complemented
6C2×C11×#379C211yesmaximal, characteristic
7C26×C11C2211yescharacteristic
8C22×C11×C22⋊C4—22no—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11—24no—
12C22×C22⋊Dic11C2212yes—
13C22×C22⋊Dic11C2212yes—
14C2×#66977—22no—
15#10623014—22no—
16#10623014—24no—
17#10623014C2214yescomplemented
18C2×#66931—24no—
19C11×#379—22no—
20C11×#379C2214yes—
21#10622860—24no—
22#10622860C2218yes—
23#10622165C2218yescomplemented
24#10622164C2214yescomplemented
25C25×C11—22no—
26C25×C11—21no—
27C25×C11—22no—
28C25×C11—21no—
29C25×C11—22no—
30C25×C11—24no—
31C25×C11—48no—
32C25×C11Q814yescomplemented
33C25×C11C2312yes—
34C25×C11C2311yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C23×Dic11—22no—
38C23×Dic11D414yes—
39C22×Dic22—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—28no—
45C2×C11×C22⋊C4—48no—
46C2×C11×C22⋊C4D412yes—
47C2×C11×C22⋊C4C2312yes—
48C2×C11×C22⋊C4C2312yes—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—216no—
57C2×C22⋊Dic11—416no—
58C2×C22⋊Dic11D414yes—
59C2×C22⋊Dic11C2314yes—
60C2×C22⋊Dic11C2314yes—
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—216no—
69C24×C11—28no—
70C24×C11—28no—
71C24×C11—24no—
72C24×C11—24no—
73C24×C11—22no—
74C24×C11—28no—
75C24×C11—24no—
76C24×C11—22no—
77C24×C11—24no—
78C24×C11—416no—
79C24×C11—44no—
80C24×C11—48no—
81C24×C11—48no—
82C24×C11—44no—
83C24×C11—416no—
84C24×C11—48no—
85C24×C11—432no—
86C24×C11—416no—
87C24×C11—41no—
88C24×C11—42no—
89C24×C11—41no—
90C24×C11—44no—
91C24×C11—42no—
92C24×C11—44no—
93C24×C11—42no—
94C24×C11C2×D412yes—
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D412yes—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×Q812yes—
99C24×C11C2×Q814yescomplemented
100C24×C11#4112yes—
101C24×C11#4114yes—
102C24×C11C2411yescharacteristic
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D414yes—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—48no—
114C22×Dic11—48no—
115C22×Dic11—44no—
116C22×Dic11C2×D418yes—
117C2×Dic22—28no—
118C2×Dic22—84no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—416no—
123C11×C22⋊C4—42no—
124C22⋊Dic11—24no—
125C22⋊Dic11—24no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—24no—
130C22⋊Dic11—432no—
131C22⋊Dic11—44no—
132C4⋊Dic11—28no—
133Dic11⋊C4—216no—
134C2×#543—111no—
135C2×#379—112no—
136C2×#379D1111yescharacteristic
137#2029—118no—
138C2×#342—112no—
139C2×#342—111no—
140C23×C11—28no—
141C23×C11—24no—
142C23×C11—216no—
143C23×C11—28no—
144C23×C11—232no—
145C23×C11—216no—
146C23×C11—28no—
147C23×C11—24no—
148C23×C11—44no—
149C23×C11—42no—
150C23×C11—44no—
151C23×C11—48no—
152C23×C11—44no—
153C23×C11—48no—
154C23×C11—42no—
155C23×C11—44no—
156C23×C11—48no—
157C23×C11—48no—
158C23×C11—416no—
159C23×C11—416no—
160C23×C11—416no—
161C23×C11—48no—
162C23×C11—432no—
163C23×C11—432no—
164C23×C11—416no—
165C23×C11—48no—
166C23×C11—416no—
167C23×C11—432no—
168C23×C11—416no—
169C23×C11—42no—
170C23×C11—44no—
171C23×C11—42no—
172C23×C11—48no—
173C23×C11—44no—
174C23×C11—44no—
175C23×C11—48no—
176C23×C11#12011yescharacteristic
177C23×C11#12012yes—
178C23×C11#12011yescharacteristic
179C23×C11C22⋊Q814yes—
180C23×C11C22⋊Q814yes—
181C23×C11C22⋊Q812yes—
182C23×C11C22⋊Q812yes—
183C23×C11#12414yes—
184C23×C11#12414yes—
185C23×C11#12412yes—
186C23×C11#12412yes—
187C23×C11C22×D412yes—
188C23×C11C22×D411yescharacteristic
189C23×C11C22×Q811yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4112yes—
192C2×C4×C11—24no—
193C2×C4×C11—44no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—42no—
197C2×C4×C11—82no—
198C2×C4×C11—84no—
199C2×Dic11—28no—
200C2×Dic11—48no—
201C2×Dic11—48no—
202C2×Dic11—48no—
203C2×Dic11—44no—
204C2×Dic11—84no—
205C2×Dic11—88no—
206Dic22—88no—
207C26C2×D1111yescharacteristic
208#543—114no—
209#543—224no—
210#543—222no—
211C2×C22⋊Q8—224no—
212C2×C22⋊Q8—222no—
213C22×C22⋊C4—22no—
214C22×C22⋊C4—112no—
215C22×C22⋊C4—112no—
216C22×C22⋊C4—224no—
217C22×C22⋊C4C2×D1111yescharacteristic
218C22×C22⋊C4C2×D1111yescharacteristic
219#379—22no—
220#379—118no—
221#379—224no—
222#379C2×D1114yes—
223#342—114no—
224#342—118no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—24no—
228C22×C11—24no—
229C22×C11—24no—
230C22×C11—28no—
231C22×C11—24no—
232C22×C11—28no—
233C22×C11—216no—
234C22×C11—28no—
235C22×C11—44no—
236C22×C11—42no—
237C22×C11—44no—
238C22×C11—42no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—42no—
242C22×C11—416no—
243C22×C11—48no—
244C22×C11—48no—
245C22×C11—44no—
246C22×C11—416no—
247C22×C11—432no—
248C22×C11—44no—
249C22×C11—48no—
250C22×C11—416no—
251C22×C11#39312yes—
252C22×C11#39314yes—
253C22×C11#39312yes—
254C22×C11B(4,𝔽2)14yes—
255C22×C11C2×#12011yescharacteristic
256C22×C11C2×C22⋊Q812yes—
257C22×C11C2×C22⋊Q811yescharacteristic
258C22×C11C2×#12412yes—
259C22×C11C2×#12411yescharacteristic
260C4×C11—44no—
261C4×C11—82no—
262Dic11—48no—
263Dic11—84no—
264C25—22no—
265C25—21no—
266C25—22no—
267C25—22no—
268C25—24no—
269C25—21no—
270C25—48no—
271C25Dic2214yescomplemented
272C25C22×D1112yes—
273C25C22×D1111yescharacteristic
274C22×Q8—222no—
275C23×C4—21no—
276C23×C4—114no—
277C23×C4—222no—
278C23×C4C22⋊D1112yes—
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—21no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—48no—
291C2×C22⋊C4—114no—
292C2×C22⋊C4—114no—
293C2×C22⋊C4—114no—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—224no—
299C2×C22⋊C4—224no—
300C2×C22⋊C4—2216no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—4416no—
303C2×C22⋊C4C22⋊D1112yes—
304C2×C22⋊C4C22×D1112yes—
305C2×C22⋊C4C22×D1112yes—
306C2×C11—22no—
307C2×C11—21no—
308C2×C11—22no—
309C2×C11—21no—
310C2×C11—22no—
311C2×C11—24no—
312C2×C11—48no—
313C2×C11#202914yescomplemented
314C2×C11C2×#39311yescharacteristic
315C2×C11C2×B(4,𝔽2)12yes—
316C24—28no—
317C24—216no—
318C24—28no—
319C24—24no—
320C24—24no—
321C24—22no—
322C24—28no—
323C24—24no—
324C24—22no—
325C24—24no—
326C24—48no—
327C24—44no—
328C24—416no—
329C24—44no—
330C24—48no—
331C24—48no—
332C24—416no—
333C24—416no—
334C24—432no—
335C24—44no—
336C24—44no—
337C24—42no—
338C24—42no—
339C24—42no—
340C24—41no—
341C24—41no—
342C24C2×Dic2212yes—
343C24C2×Dic2214yescomplemented
344C24#433912yes—
345C24D4×D1112yes—
346C24D4×D1112yes—
347C24#434114yes—
348C24C2×C22⋊D1111yescharacteristic
349C24C2×C22⋊D1111yescharacteristic
350C24C23×D1111yescharacteristic
351C2×Q8—228no—
352C2×Q8—884no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4—42no—
359C22×C4—118no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4—224no—
363C22×C4—448no—
364C22×C4—448no—
365C22×C4—444no—
366C22×C4C2×C22⋊D1114yes—
367C4⋊C4—2216no—
368C4⋊C4—228no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—416no—
373C22⋊C4—42no—
374C22⋊C4—224no—
375C22⋊C4—224no—
376C22⋊C4—224no—
377C22⋊C4—224no—
378C22⋊C4—224no—
379C22⋊C4—224no—
380C22⋊C4—4432no—
381C22⋊C4—444no—
382C11C2×#202911yescharacteristic, complemented, Sylow
383C23—24no—
384C23—28no—
385C23—28no—
386C23—216no—
387C23—232no—
388C23—216no—
389C23—28no—
390C23—24no—
391C23—44no—
392C23—48no—
393C23—44no—
394C23—44no—
395C23—48no—
396C23—42no—
397C23—42no—
398C23—416no—
399C23—432no—
400C23—416no—
401C23—48no—
402C23—44no—
403C23—48no—
404C23—48no—
405C23—416no—
406C23—432no—
407C23—416no—
408C23—48no—
409C23—416no—
410C23—432no—
411C23—416no—
412C23—44no—
413C23—48no—
414C23—44no—
415C23—44no—
416C23—42no—
417C23—42no—
418C23—48no—
419C23#6693114yes—
420C23#6693114yes—
421C23#6693814yes—
422C23#6693814yes—
423C23#6697712yes—
424C23#6697712yes—
425C23#6698912yes—
426C23#6698912yes—
427C23#6699012yes—
428C23#6699011yescharacteristic
429C23#6699011yescharacteristic
430C23C22×Dic2211yescharacteristic
431C23C2×#433911yescharacteristic
432C23C2×D4×D1112yes—
433C23C2×#434112yes—
434C23C22×C22⋊D1111yescharacteristic
435Q8—888no—
436C2×C4—24no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4—84no—
443C2×C4—228no—
444C2×C4—448no—
445C2×C4—448no—
446C2×C4—448no—
447C2×C4—444no—
448C2×C4—884no—
449C2×C4—888no—
450C22—24no—
451C22—28no—
452C22—28no—
453C22—24no—
454C22—22no—
455C22—22no—
456C22—24no—
457C22—24no—
458C22—216no—
459C22—28no—
460C22—44no—
461C22—44no—
462C22—42no—
463C22—42no—
464C22—41no—
465C22—41no—
466C22—42no—
467C22—48no—
468C22—416no—
469C22—48no—
470C22—44no—
471C22—416no—
472C22—432no—
473C22—44no—
474C22—416no—
475C22—48no—
476C22#1062256014yes—
477C22#1062256012yes—
478C22#1062256012yes—
479C22#1062264514yes—
480C22C2×#6693112yes—
481C22C2×#6693812yes—
482C22C2×#6697711yescharacteristic
483C22C2×#6698911yescharacteristic
484C22C2×#6699011yescharacteristic
485C4—44no—
486C4—82no—
487C4—448no—
488C4—884no—
489C2—21no—
490C2—22no—
491C2—22no—
492C2—21no—
493C2—22no—
494C2—24no—
495C2—48no—
496C2#1306978014yesdirect product factor
497C2C2×#1062256011yescharacteristic
498C2C2×#1062264512yes—
subgroupG/H
centerC23#66990
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#379C2
socleC23×C11#120
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C2×#2029
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13069780C2direct (N × H)
4. C2×#10622164C2semidirect
5. C2×#10622165C2semidirect
17. #10623014C22semidirect
23. #10622165C22semidirect
24. #10622164C22semidirect
32. C25×C11Q8semidirect
99. C24×C11C2×Q8semidirect
271. C25Dic22semidirect
313. C2×C11#2029semidirect
343. C24C2×Dic22semidirect
382. C11C2×#2029semidirect
496. C2#13069780direct (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×#106228602
#130697802
C2×#106221642
C2×#106221652
C2×C11×#3792
C2×#202911