Finite Group Databasebeta

← C2×#13067113 #14720875

Subgroups — C2×#13067113 #14720875

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C2×#10622331C211yesmaximal, characteristic
3C2×#10622262C211yesmaximal, characteristic
4#13067113C218yesmaximal, direct product factor
5C2×#10622105C211yesmaximal, characteristic
6C2×#10622176C211yesmaximal, characteristic
7C2×#10622090C211yesmaximal, characteristic
8C2×C11×#328C211yesmaximal, characteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic, complemented
11C2×#66997C411yescharacteristic, complemented
12C2×#66977C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C22×C4×Dic11—21no—
15C22×C4×Dic11C2211yescharacteristic
16#10623153—22no—
17#10623153—22no—
18#10623153C414yescomplemented
19#10623153C2214yes—
20C2×#66942—21no—
21C2×#66941C411yescharacteristic, complemented
22C2×#66940—21no—
23C2×#66940C411yescharacteristic, complemented
24C2×#66931—21no—
25C2×#66930—21no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×Dic11⋊C8—21no—
31C2×C8×Dic11—21no—
32#10622331—22no—
33#10622331C2214yes—
34#10622262—22no—
35#10622262C2214yes—
36C11×#328C2214yes—
37#10622176C2214yes—
38#10622105C2214yes—
39#10622090C2214yes—
40C22×Q8×C11C2×C411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C23×Dic11D411yescharacteristic
46C22×Dic22—21no—
47C22×Dic22C2×C411yescharacteristic
48C22×C8×C11—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8C2×C412yes—
52C11×C22⋊Q8C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57Q8×Dic11—22no—
58Q8×Dic11C2×C414yescomplemented
59#66997—22no—
60#66997C2×C414yescomplemented
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2×C411yescharacteristic
63#66977—21no—
64#66977—21no—
65#66977C2×C412yes—
66#66977C2312yes—
67C2×Dic11⋊C4—28no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—24no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—44no—
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2×C412yes—
81C2×C4×Dic11D412yes—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D412yes—
85C2×C4×Dic11C2312yes—
86C22×C11⋊C8—21no—
87#66942—24no—
88#66942—24no—
89#66941—22no—
90#66941C2×C414yescomplemented
91#66940—24no—
92#66940—22no—
93#66940—24no—
94#66940C2×C414yescomplemented
95#66931—24no—
96#66931—24no—
97#66930—24no—
98#66930—24no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8C2312yes—
101C11×#95—21no—
102C11×#95C2312yes—
103C11⋊#95—21no—
104C11⋊#95C2312yes—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)C2312yes—
107Dic11⋊C8—24no—
108C8×Dic11—24no—
109C2×#1503—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—42no—
113C2×Q8×C11C22×C412yes—
114C22×C4×C11—24no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11C22⋊C412yes—
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C412yes—
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140C22×Dic11SD1614yes—
141C22×Dic11Q1614yes—
142C22×Dic11C2×D412yes—
143C22×Dic11C2×D412yes—
144C2×Dic22—24no—
145C2×Dic22—21no—
146C2×Dic22—42no—
147C2×Dic22—44no—
148C2×Dic22C22×C412yes—
149C2×C8×C11—22no—
150C2×C8×C11—42no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C22×C412yes—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C22⋊Dic11—22no—
158C22⋊Dic11—22no—
159C4⋊Dic11—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11C22×C412yes—
162Dic11⋊C4—216no—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—22no—
168Dic11⋊C4—22no—
169C4×Dic11—24no—
170C4×Dic11—24no—
171C4×Dic11—48no—
172C4×Dic11C22⋊C412yes—
173C4×Dic11C22⋊C412yes—
174C4×Dic11C22⋊C412yes—
175C4×Dic11C22⋊C412yes—
176C4×Dic11C22×C412yes—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—42no—
182C2×#533—111no—
183C2×#431—111no—
184C2×C4×C4⋊C4—111no—
185#1503—118no—
186C2×#328—111no—
187C2×#328—111no—
188C2×#328—111no—
189C2×#328D1111yescharacteristic
190C23×C11—22no—
191C23×C11—22no—
192C23×C11C2×C22⋊C411yescharacteristic
193C23×C11C2×C22⋊C411yescharacteristic
194C23×C11C2×SD1612yes—
195C23×C11C2×Q1612yes—
196C23×C11C22×D411yescharacteristic
197Q8×C11—42no—
198Q8×C11—42no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—42no—
224C2×Dic11—48no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11#10318yes—
229C2×Dic11#10314yes—
230C2×Dic11#10314yes—
231C2×Dic11#10414yes—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236C2×Dic11C2×SD1614yes—
237C2×Dic11C2×Q1614yes—
238Dic22—42no—
239Dic22—48no—
240Dic22—42no—
241C8×C11—42no—
242C11⋊C8—42no—
243#533—114no—
244#533—114no—
245#533—222no—
246#533—222no—
247C2×C4⋊Q8—111no—
248C2×C4⋊Q8—111no—
249C2×#125—221no—
250C2×C22⋊Q8—111no—
251C2×C22⋊Q8—221no—
252C2×C22⋊Q8C2×D1111yescharacteristic
253C2×C4×Q8—111no—
254C2×C4×Q8—111no—
255C2×C4×Q8—221no—
256C2×#117—221no—
257C22×C4⋊C4—221no—
258C22×C42—111no—
259C22×C42—221no—
260#431—114no—
261#431—222no—
262C2×C4⋊C8—221no—
263C2×C22⋊C8—111no—
264C2×C22⋊C8C2×D1111yescharacteristic
265C2×C4×C8—221no—
266C4×C4⋊C4—114no—
267C4×C4⋊C4—222no—
268C2×#95—111no—
269C2×#95C2×D1111yescharacteristic
270#328—114no—
271#328—114no—
272#328—114no—
273#328C2×D1114yes—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11#41012yes—
281C22×C11C2×#10312yes—
282C22×C11C2×#10312yes—
283C22×C11C2×#10412yes—
284C22×C11C22×C22⋊C411yescharacteristic
285C22×C11C22×SD1611yescharacteristic
286C22×C11C22×Q1611yescharacteristic
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—44no—
292C4×C11—42no—
293C4×C11—42no—
294Dic11—22no—
295Dic11—44no—
296Dic11—42no—
297Dic11—42no—
298Dic11C2×#10314yes—
299Dic11C2×#10314yes—
300Dic11C2×#10414yes—
301C22×Q8—111no—
302C22×Q8—221no—
303C22×Q8C4×D1111yescharacteristic
304C23×C4—21no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—221no—
308C23×C4C22×D1111yescharacteristic
309C22×C8—21no—
310C22×C8—221no—
311C4⋊Q8—114no—
312C4⋊Q8—114no—
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315#125—224no—
316#125—224no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—112no—
320C22⋊Q8—112no—
321C22⋊Q8—224no—
322C22⋊Q8—224no—
323C22⋊Q8—221no—
324C22⋊Q8—221no—
325C22⋊Q8C4×D1112yes—
326C22⋊Q8C22×D1112yes—
327C4×Q8—114no—
328C4×Q8—114no—
329C4×Q8—222no—
330C4×Q8—224no—
331C4×Q8—224no—
332C4×Q8—222no—
333#117—224no—
334#117—224no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4C4×D1111yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—221no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—112no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—112no—
354C2×C42—112no—
355C2×C42—112no—
356C2×C42—221no—
357C2×C42—221no—
358C2×C42—224no—
359C2×C42—444no—
360C4⋊C8—224no—
361C22⋊C8—21no—
362C22⋊C8—112no—
363C22⋊C8—221no—
364C22⋊C8C22×D1112yes—
365C4×C8—224no—
366#95—21no—
367#95—112no—
368#95—221no—
369#95C22×D1112yes—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—22no—
373C2×C11#150314yescomplemented
374C2×C11C2×#41011yescharacteristic
375C2×C11C22×#10311yescharacteristic
376C2×C11C22×#10411yescharacteristic
377C24D4×D1111yescharacteristic
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—112no—
381C2×Q8—224no—
382C2×Q8—221no—
383C2×Q8—442no—
384C2×Q8—444no—
385C2×Q8C2×C4×D1112yes—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—112no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—111no—
402C22×C4—112no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4C2×C4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416C2×C8—22no—
417C2×C8—42no—
418C2×C8—222no—
419C2×C8—442no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—112no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—2216no—
430C4⋊C4—221no—
431C4⋊C4—222no—
432C4⋊C4—222no—
433C4⋊C4C2×C4×D1112yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—222no—
437C22⋊C4—222no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—112no—
442C42—112no—
443C42—112no—
444C42—112no—
445C42—112no—
446C42—224no—
447C42—224no—
448C42—448no—
449C11C2×#150311yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23C22⋊C4×D1111yescharacteristic
453C23C22⋊C4×D1111yescharacteristic
454C23SD16×D1112yes—
455C23Q16×D1112yes—
456C23C2×D4×D1111yescharacteristic
457Q8—42no—
458Q8—42no—
459Q8—442no—
460Q8—442no—
461Q8—448no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—114no—
480C2×C4—114no—
481C2×C4—118no—
482C2×C4—114no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—112no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—222no—
489C2×C4—224no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—442no—
493C2×C4—448no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4C22⋊C4×D1111yescharacteristic
498C2×C4C22⋊C4×D1111yescharacteristic
499C2×C4C22×C4×D1111yescharacteristic
500C2×C4C2×D4×D1111yescharacteristic
501C8—42no—
502C8—442no—
503C22—21no—
504C22—21no—
505C22—24no—
506C22—24no—
507C22—21no—
508C22—21no—
509C22#1062235312yes—
510C22D11×#10312yes—
511C22D11×#10312yes—
512C22D11×#10412yes—
513C22C2×C22⋊C4×D1111yescharacteristic
514C22C2×SD16×D1111yescharacteristic
515C22C2×Q16×D1111yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—44no—
521C4—42no—
522C4—42no—
523C4—114no—
524C4—114no—
525C4—114no—
526C4—222no—
527C4—444no—
528C4—442no—
529C4—442no—
530C2—21no—
531C2—21no—
532C2—22no—
533C2#1306711314yesdirect product factor
534C2C2×#1062235311yescharacteristic
535C2C2×D11×#10311yescharacteristic
536C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#328D11
hypocenterC11C2×#1503
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. #13067113C2direct (N × H)
10. C2×Q8×Dic11C4semidirect
11. C2×#66997C4semidirect
18. #10623153C4semidirect
21. C2×#66941C4semidirect
23. C2×#66940C4semidirect
58. Q8×Dic11C2×C4semidirect
60. #66997C2×C4semidirect
90. #66941C2×C4semidirect
94. #66940C2×C4semidirect
373. C2×C11#1503semidirect
449. C11C2×#1503semidirect
533. C2#13067113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106223312
C2×#106222622
#130671132
C2×#106221052
C2×#106221762
C2×#106220902
C2×C11×#3282
C2×#150311